numberOfDominoTilings.ipynb

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  "metadata": {
    "colab": {
      "name": "numberOfDominoTilings.ipynb",
      "provenance": [],
      "collapsed_sections": [
        "HNiGI2vkT2QJ",
        "IcOw1-YKKtZ0"
      ],
      "toc_visible": true,
      "authorship_tag": "ABX9TyMo7cInHyT07a5mM16ilJ01",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/ptleskin/numberOfDominoTilings/blob/main/numberOfDominoTilings.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0e-Kn_QPPdTc"
      },
      "source": [
        "This Colab Notebook was inspired by Mathologer's video [*The ARCTIC CIRCLE THEOREM or Why do physicists play dominoes?*](https://www.youtube.com/watch?v=Yy7Q8IWNfHM&t=1856s).\n",
        "\n",
        "The codes provided contain functions for calculating the number of tilings and downloading an animated example of possible ways to tile a grid of a specified shape. \n",
        "\n",
        "petri.leskinen@icloud.com, December 27, 2020."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HNiGI2vkT2QJ"
      },
      "source": [
        "# install the dependencies"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YRoHM-HGTwqu"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AjtE45Qd19rf",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "7d0e8a84-7e09-4981-bd48-3484ad53cea0"
      },
      "source": [
        "import numpy as np\n",
        "import scipy.linalg as linalg\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "from matplotlib.path import Path\n",
        "import matplotlib.patches as patches\n",
        "\n",
        "from itertools import permutations, product\n",
        "from collections import defaultdict\n",
        "!apt install imagemagick\n",
        "\n",
        "!mkdir images"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Reading package lists... Done\n",
            "Building dependency tree       \n",
            "Reading state information... Done\n",
            "The following additional packages will be installed:\n",
            "  fonts-droid-fallback fonts-noto-mono ghostscript gsfonts\n",
            "  imagemagick-6-common imagemagick-6.q16 libcupsfilters1 libcupsimage2\n",
            "  libdjvulibre-text libdjvulibre21 libgs9 libgs9-common libijs-0.35\n",
            "  libjbig2dec0 liblqr-1-0 libmagickcore-6.q16-3 libmagickcore-6.q16-3-extra\n",
            "  libmagickwand-6.q16-3 libnetpbm10 libwmf0.2-7 netpbm poppler-data\n",
            "Suggested packages:\n",
            "  fonts-noto ghostscript-x imagemagick-doc autotrace cups-bsd | lpr | lprng\n",
            "  enscript gimp gnuplot grads hp2xx html2ps libwmf-bin mplayer povray radiance\n",
            "  sane-utils texlive-base-bin transfig ufraw-batch inkscape libjxr-tools\n",
            "  libwmf0.2-7-gtk poppler-utils fonts-japanese-mincho | fonts-ipafont-mincho\n",
            "  fonts-japanese-gothic | fonts-ipafont-gothic fonts-arphic-ukai\n",
            "  fonts-arphic-uming fonts-nanum\n",
            "The following NEW packages will be installed:\n",
            "  fonts-droid-fallback fonts-noto-mono ghostscript gsfonts imagemagick\n",
            "  imagemagick-6-common imagemagick-6.q16 libcupsfilters1 libcupsimage2\n",
            "  libdjvulibre-text libdjvulibre21 libgs9 libgs9-common libijs-0.35\n",
            "  libjbig2dec0 liblqr-1-0 libmagickcore-6.q16-3 libmagickcore-6.q16-3-extra\n",
            "  libmagickwand-6.q16-3 libnetpbm10 libwmf0.2-7 netpbm poppler-data\n",
            "0 upgraded, 23 newly installed, 0 to remove and 15 not upgraded.\n",
            "Need to get 18.4 MB of archives.\n",
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      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IcOw1-YKKtZ0"
      },
      "source": [
        "## Define the needed functions"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3NBmsR3P27TD"
      },
      "source": [
        "def calculateMatrix(M):\n",
        "  '''\n",
        "  Calculates:\n",
        "  A: the complex 'adjacency' matrix, where |det(A)| = number of possible tilings\n",
        "  B: matrix of possible domino locations\n",
        "  N: a lookup table of which cell indices (-n, -n+1, ..., -1, 1, 2, ..., n-1, n)\n",
        "    corresponds to which cell coordinate\n",
        "  '''\n",
        "  M = np.array(M)\n",
        "  N = np.zeros(M.shape, dtype=int)\n",
        "  ym, xm = N.shape\n",
        "\n",
        "  # index the 'black' (positive int) and 'white' (negative int) cell\n",
        "  i, j = 0, 0\n",
        "  for y in range(ym):\n",
        "    for x in range(xm):\n",
        "      if M[y][x]:\n",
        "        if (x+y)%2:\n",
        "          i += 1\n",
        "          N[y][x] = i\n",
        "        else:\n",
        "          j -= 1\n",
        "          N[y][x] = j\n",
        "  s = int(np.max(N))\n",
        "  A = np.zeros((s, s), dtype=complex)\n",
        "  B = np.zeros((s, s), dtype=object)\n",
        "\n",
        "  ym, xm = N.shape\n",
        "  # A: 'adjacency' matrix with 1 for horizontal pair, and i for vertical pair:\n",
        "  for y in range(ym):\n",
        "    for x in range(xm):\n",
        "      xn = N[y][x]\n",
        "      if xn != 0:\n",
        "        if x+1<xm:\n",
        "          # horizontal pair, 1\n",
        "          yn = N[y][x+1]\n",
        "          if yn<0:\n",
        "            # print(yn, xn)\n",
        "            A[xn-1][-yn-1] = 1\n",
        "            B[xn-1][-yn-1] = (xn, yn)\n",
        "          elif yn>0:\n",
        "            # print(xn, yn)\n",
        "            A[yn-1][-xn-1] = 1\n",
        "            B[yn-1][-xn-1] = (xn, yn)\n",
        "        if y+1<ym:\n",
        "          # vertical pair, i\n",
        "          yn = N[y+1][x]\n",
        "          if yn<0:\n",
        "            A[xn-1][-yn-1] = complex(0,1)\n",
        "            B[xn-1][-yn-1] = (xn, yn)\n",
        "          elif yn>0:\n",
        "            A[yn-1][-xn-1] = complex(0,1)\n",
        "            B[yn-1][-xn-1] = (xn, yn)\n",
        "  return A, B, N\n",
        "\n",
        "\n",
        "def tuple2rectangle(tpl, N):\n",
        "  '''\n",
        "  Convert a cell pair e.g. (2, -6)\n",
        "    into a polyline path on corresponding rectangle\n",
        "  Returns: (polyline, vertical) where\n",
        "    vertical = True, if the tile is in a vertical position, False if horizontal\n",
        "  '''\n",
        "  [y],[x] = np.where(N==tpl[0])\n",
        "  [y2],[x2] = np.where(N==tpl[1])\n",
        "  x, x2 = sorted([x, x2])\n",
        "  y, y2 = sorted([y, y2])\n",
        "  return [(x, y), (x2+1, y), (x2+1, y2+1), (x, y2+1), (x, y)], x!=x2\n",
        "\n",
        "\n",
        "def drawTiling(rects, ax, vcolor='orange', hcolor='blue'):\n",
        "  codes = [\n",
        "    Path.MOVETO,\n",
        "    Path.LINETO,\n",
        "    Path.LINETO,\n",
        "    Path.LINETO,\n",
        "    Path.CLOSEPOLY,\n",
        "  ]\n",
        "  for tpl in rects:\n",
        "    verts, vertical = tuple2rectangle(tpl, N)\n",
        "    \n",
        "    path = Path(verts, codes)\n",
        "    patch = patches.PathPatch(path, facecolor=vcolor if vertical else hcolor, lw=1)\n",
        "    ax.add_patch(patch)\n",
        "    ax.set_xlim(0, M.shape[0])\n",
        "    ax.set_ylim(0, M.shape[1])\n",
        "    ax.axis('equal')\n",
        "\n",
        "\n",
        "def numberOfTilings(M):\n",
        "    A, _, _ = calculateMatrix(M)\n",
        "    return int(0.5+abs(linalg.det(A)))\n",
        "\n",
        "\n",
        "def cell_product(*args, res = []):\n",
        "    '''\n",
        "    This custom generator returns the non-zero cells from the matrix M \n",
        "    similarily as the partial sums of the determinant\n",
        "    so that all values are sampled from distinct rows and columns.\n",
        "\n",
        "    e.g. cell_product([0,1],[1,3])) = [[0, 1], [0, 3], [1, 3]]\n",
        "    '''\n",
        "    if len(args):\n",
        "      for x in args[0]:\n",
        "        if not x in res:\n",
        "          yield from cell_product(*args[1:], res = res+[x])\n",
        "    else:\n",
        "      yield res\n",
        "\n",
        "\n",
        "def getTilings(B):\n",
        "    '''\n",
        "    Generator for all possible tilings\n",
        "    '''\n",
        "    # pick the non-zero matrix values\n",
        "    # nonzeros = {<row_number>: [<columns with nonzero values>]}\n",
        "    nonzeros= defaultdict(list)\n",
        "    for y,x in zip(*np.where(B != 0)):\n",
        "      nonzeros[y].append(x)\n",
        "\n",
        "    ''' # brute force solution\n",
        "    for arr in product(*nonzeros.values()):\n",
        "      # pick only the sequences where all values are distinct, e.g. corresponding to distinct columns of the matrix\n",
        "      if len(arr)==len(set(arr)):\n",
        "        yield [B[y][x] for y,x in enumerate(arr)]\n",
        "    '''\n",
        "    for arr in cell_product(*nonzeros.values()):\n",
        "        yield [B[y][x] for y,x in enumerate(arr)]\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Iovc-kosjqus"
      },
      "source": [
        "# these function are for representing the grids\n",
        "import pandas as pd\n",
        "\n",
        "# show matrices with chessboard coloring\n",
        "def apply_chessboard(val):\n",
        "    r = val.copy()\n",
        "    for i, row in r.iterrows():\n",
        "      for j, x in row.iteritems():\n",
        "        if x==0:\n",
        "          st = 'color: lightgrey'\n",
        "        else:\n",
        "          st = 'color: white; background-color: green' if (i+j)%2 else 'color: white; background-color: black'\n",
        "        r.loc[i,j] = st\n",
        "    return r\n",
        "\n",
        "def showMatrix(M):\n",
        "  df=pd.DataFrame(M)\n",
        "  return df.style.apply(apply_chessboard, axis=None).set_properties(**{'width':'2em', 'height':'2em', 'text-align':'center'})#.hide_index()#.hide_columns(df.columns)\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cudGI98eQn8b"
      },
      "source": [
        "# Simple example shape as shown in the video at [11:00](https://www.youtube.com/watch?v=Yy7Q8IWNfHM&t=660s).\n",
        "\n",
        "\n",
        "Matrix M is a binary matrix, with 1 for cells being a part in the shape, and 0 for cells outside the shape."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 232
        },
        "id": "giE4jIo24elQ",
        "outputId": "f7d04ad6-32f6-4b96-a9ab-6e07ce9c5f1a"
      },
      "source": [
        "M = [[1, 1, 0, 0, 1, 1],\n",
        "     [1, 1, 1, 1, 1, 1],\n",
        "     [1, 1, 1, 1, 1, 1],\n",
        "     [0, 1, 1, 1, 0, 0],\n",
        "     [0, 1, 1, 1, 0, 0],\n",
        "     [0, 0, 0, 0, 0, 0]\n",
        "     ]\n",
        "\n",
        "M = np.array(M)\n",
        "A,B,N = calculateMatrix(M)\n",
        "display(showMatrix(M))"
      ],
      "execution_count": 44,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<style  type=\"text/css\" >\n",
              "#T_be7e13be_4848_11eb_aa0b_0242ac1c0002row0_col0,#T_be7e13be_4848_11eb_aa0b_0242ac1c0002row0_col4,#T_be7e13be_4848_11eb_aa0b_0242ac1c0002row1_col1,#T_be7e13be_4848_11eb_aa0b_0242ac1c0002row1_col3,#T_be7e13be_4848_11eb_aa0b_0242ac1c0002row1_col5,#T_be7e13be_4848_11eb_aa0b_0242ac1c0002row2_col0,#T_be7e13be_4848_11eb_aa0b_0242ac1c0002row2_col2,#T_be7e13be_4848_11eb_aa0b_0242ac1c0002row2_col4,#T_be7e13be_4848_11eb_aa0b_0242ac1c0002row3_col1,#T_be7e13be_4848_11eb_aa0b_0242ac1c0002row3_col3,#T_be7e13be_4848_11eb_aa0b_0242ac1c0002row4_col2{\n",
              "            color:  white;\n",
              "             background-color:  black;\n",
              "            width:  2em;\n",
              "            height:  2em;\n",
              "            text-align:  center;\n",
              "        }#T_be7e13be_4848_11eb_aa0b_0242ac1c0002row0_col1,#T_be7e13be_4848_11eb_aa0b_0242ac1c0002row0_col5,#T_be7e13be_4848_11eb_aa0b_0242ac1c0002row1_col0,#T_be7e13be_4848_11eb_aa0b_0242ac1c0002row1_col2,#T_be7e13be_4848_11eb_aa0b_0242ac1c0002row1_col4,#T_be7e13be_4848_11eb_aa0b_0242ac1c0002row2_col1,#T_be7e13be_4848_11eb_aa0b_0242ac1c0002row2_col3,#T_be7e13be_4848_11eb_aa0b_0242ac1c0002row2_col5,#T_be7e13be_4848_11eb_aa0b_0242ac1c0002row3_col2,#T_be7e13be_4848_11eb_aa0b_0242ac1c0002row4_col1,#T_be7e13be_4848_11eb_aa0b_0242ac1c0002row4_col3{\n",
              "            color:  white;\n",
              "             background-color:  green;\n",
              "            width:  2em;\n",
              "            height:  2em;\n",
              "            text-align:  center;\n",
              "        }#T_be7e13be_4848_11eb_aa0b_0242ac1c0002row0_col2,#T_be7e13be_4848_11eb_aa0b_0242ac1c0002row0_col3,#T_be7e13be_4848_11eb_aa0b_0242ac1c0002row3_col0,#T_be7e13be_4848_11eb_aa0b_0242ac1c0002row3_col4,#T_be7e13be_4848_11eb_aa0b_0242ac1c0002row3_col5,#T_be7e13be_4848_11eb_aa0b_0242ac1c0002row4_col0,#T_be7e13be_4848_11eb_aa0b_0242ac1c0002row4_col4,#T_be7e13be_4848_11eb_aa0b_0242ac1c0002row4_col5,#T_be7e13be_4848_11eb_aa0b_0242ac1c0002row5_col0,#T_be7e13be_4848_11eb_aa0b_0242ac1c0002row5_col1,#T_be7e13be_4848_11eb_aa0b_0242ac1c0002row5_col2,#T_be7e13be_4848_11eb_aa0b_0242ac1c0002row5_col3,#T_be7e13be_4848_11eb_aa0b_0242ac1c0002row5_col4,#T_be7e13be_4848_11eb_aa0b_0242ac1c0002row5_col5{\n",
              "            color:  lightgrey;\n",
              "            width:  2em;\n",
              "            height:  2em;\n",
              "            text-align:  center;\n",
              "        }</style><table id=\"T_be7e13be_4848_11eb_aa0b_0242ac1c0002\" ><thead>    <tr>        <th class=\"blank level0\" ></th>        <th class=\"col_heading level0 col0\" >0</th>        <th class=\"col_heading level0 col1\" >1</th>        <th class=\"col_heading level0 col2\" >2</th>        <th class=\"col_heading level0 col3\" >3</th>        <th class=\"col_heading level0 col4\" >4</th>        <th class=\"col_heading level0 col5\" >5</th>    </tr></thead><tbody>\n",
              "                <tr>\n",
              "                        <th id=\"T_be7e13be_4848_11eb_aa0b_0242ac1c0002level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
              "                        <td id=\"T_be7e13be_4848_11eb_aa0b_0242ac1c0002row0_col0\" class=\"data row0 col0\" >1</td>\n",
              "                        <td id=\"T_be7e13be_4848_11eb_aa0b_0242ac1c0002row0_col1\" class=\"data row0 col1\" >1</td>\n",
              "                        <td id=\"T_be7e13be_4848_11eb_aa0b_0242ac1c0002row0_col2\" class=\"data row0 col2\" >0</td>\n",
              "                        <td id=\"T_be7e13be_4848_11eb_aa0b_0242ac1c0002row0_col3\" class=\"data row0 col3\" >0</td>\n",
              "                        <td id=\"T_be7e13be_4848_11eb_aa0b_0242ac1c0002row0_col4\" class=\"data row0 col4\" >1</td>\n",
              "                        <td id=\"T_be7e13be_4848_11eb_aa0b_0242ac1c0002row0_col5\" class=\"data row0 col5\" >1</td>\n",
              "            </tr>\n",
              "            <tr>\n",
              "                        <th id=\"T_be7e13be_4848_11eb_aa0b_0242ac1c0002level0_row1\" class=\"row_heading level0 row1\" >1</th>\n",
              "                        <td id=\"T_be7e13be_4848_11eb_aa0b_0242ac1c0002row1_col0\" class=\"data row1 col0\" >1</td>\n",
              "                        <td id=\"T_be7e13be_4848_11eb_aa0b_0242ac1c0002row1_col1\" class=\"data row1 col1\" >1</td>\n",
              "                        <td id=\"T_be7e13be_4848_11eb_aa0b_0242ac1c0002row1_col2\" class=\"data row1 col2\" >1</td>\n",
              "                        <td id=\"T_be7e13be_4848_11eb_aa0b_0242ac1c0002row1_col3\" class=\"data row1 col3\" >1</td>\n",
              "                        <td id=\"T_be7e13be_4848_11eb_aa0b_0242ac1c0002row1_col4\" class=\"data row1 col4\" >1</td>\n",
              "                        <td id=\"T_be7e13be_4848_11eb_aa0b_0242ac1c0002row1_col5\" class=\"data row1 col5\" >1</td>\n",
              "            </tr>\n",
              "            <tr>\n",
              "                        <th id=\"T_be7e13be_4848_11eb_aa0b_0242ac1c0002level0_row2\" class=\"row_heading level0 row2\" >2</th>\n",
              "                        <td id=\"T_be7e13be_4848_11eb_aa0b_0242ac1c0002row2_col0\" class=\"data row2 col0\" >1</td>\n",
              "                        <td id=\"T_be7e13be_4848_11eb_aa0b_0242ac1c0002row2_col1\" class=\"data row2 col1\" >1</td>\n",
              "                        <td id=\"T_be7e13be_4848_11eb_aa0b_0242ac1c0002row2_col2\" class=\"data row2 col2\" >1</td>\n",
              "                        <td id=\"T_be7e13be_4848_11eb_aa0b_0242ac1c0002row2_col3\" class=\"data row2 col3\" >1</td>\n",
              "                        <td id=\"T_be7e13be_4848_11eb_aa0b_0242ac1c0002row2_col4\" class=\"data row2 col4\" >1</td>\n",
              "                        <td id=\"T_be7e13be_4848_11eb_aa0b_0242ac1c0002row2_col5\" class=\"data row2 col5\" >1</td>\n",
              "            </tr>\n",
              "            <tr>\n",
              "                        <th id=\"T_be7e13be_4848_11eb_aa0b_0242ac1c0002level0_row3\" class=\"row_heading level0 row3\" >3</th>\n",
              "                        <td id=\"T_be7e13be_4848_11eb_aa0b_0242ac1c0002row3_col0\" class=\"data row3 col0\" >0</td>\n",
              "                        <td id=\"T_be7e13be_4848_11eb_aa0b_0242ac1c0002row3_col1\" class=\"data row3 col1\" >1</td>\n",
              "                        <td id=\"T_be7e13be_4848_11eb_aa0b_0242ac1c0002row3_col2\" class=\"data row3 col2\" >1</td>\n",
              "                        <td id=\"T_be7e13be_4848_11eb_aa0b_0242ac1c0002row3_col3\" class=\"data row3 col3\" >1</td>\n",
              "                        <td id=\"T_be7e13be_4848_11eb_aa0b_0242ac1c0002row3_col4\" class=\"data row3 col4\" >0</td>\n",
              "                        <td id=\"T_be7e13be_4848_11eb_aa0b_0242ac1c0002row3_col5\" class=\"data row3 col5\" >0</td>\n",
              "            </tr>\n",
              "            <tr>\n",
              "                        <th id=\"T_be7e13be_4848_11eb_aa0b_0242ac1c0002level0_row4\" class=\"row_heading level0 row4\" >4</th>\n",
              "                        <td id=\"T_be7e13be_4848_11eb_aa0b_0242ac1c0002row4_col0\" class=\"data row4 col0\" >0</td>\n",
              "                        <td id=\"T_be7e13be_4848_11eb_aa0b_0242ac1c0002row4_col1\" class=\"data row4 col1\" >1</td>\n",
              "                        <td id=\"T_be7e13be_4848_11eb_aa0b_0242ac1c0002row4_col2\" class=\"data row4 col2\" >1</td>\n",
              "                        <td id=\"T_be7e13be_4848_11eb_aa0b_0242ac1c0002row4_col3\" class=\"data row4 col3\" >1</td>\n",
              "                        <td id=\"T_be7e13be_4848_11eb_aa0b_0242ac1c0002row4_col4\" class=\"data row4 col4\" >0</td>\n",
              "                        <td id=\"T_be7e13be_4848_11eb_aa0b_0242ac1c0002row4_col5\" class=\"data row4 col5\" >0</td>\n",
              "            </tr>\n",
              "            <tr>\n",
              "                        <th id=\"T_be7e13be_4848_11eb_aa0b_0242ac1c0002level0_row5\" class=\"row_heading level0 row5\" >5</th>\n",
              "                        <td id=\"T_be7e13be_4848_11eb_aa0b_0242ac1c0002row5_col0\" class=\"data row5 col0\" >0</td>\n",
              "                        <td id=\"T_be7e13be_4848_11eb_aa0b_0242ac1c0002row5_col1\" class=\"data row5 col1\" >0</td>\n",
              "                        <td id=\"T_be7e13be_4848_11eb_aa0b_0242ac1c0002row5_col2\" class=\"data row5 col2\" >0</td>\n",
              "                        <td id=\"T_be7e13be_4848_11eb_aa0b_0242ac1c0002row5_col3\" class=\"data row5 col3\" >0</td>\n",
              "                        <td id=\"T_be7e13be_4848_11eb_aa0b_0242ac1c0002row5_col4\" class=\"data row5 col4\" >0</td>\n",
              "                        <td id=\"T_be7e13be_4848_11eb_aa0b_0242ac1c0002row5_col5\" class=\"data row5 col5\" >0</td>\n",
              "            </tr>\n",
              "    </tbody></table>"
            ],
            "text/plain": [
              "<pandas.io.formats.style.Styler at 0x7ffaccb56630>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 232
        },
        "id": "mB17zuy5WfUm",
        "outputId": "3b8c939a-14aa-474f-f8e6-b50343322279"
      },
      "source": [
        "# cells with indices\n",
        "display(showMatrix(N))"
      ],
      "execution_count": 45,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<style  type=\"text/css\" >\n",
              "#T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row0_col0,#T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row0_col4,#T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row1_col1,#T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row1_col3,#T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row1_col5,#T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row2_col0,#T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row2_col2,#T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row2_col4,#T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row3_col1,#T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row3_col3,#T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row4_col2{\n",
              "            color:  white;\n",
              "             background-color:  black;\n",
              "            width:  2em;\n",
              "            height:  2em;\n",
              "            text-align:  center;\n",
              "        }#T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row0_col1,#T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row0_col5,#T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row1_col0,#T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row1_col2,#T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row1_col4,#T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row2_col1,#T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row2_col3,#T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row2_col5,#T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row3_col2,#T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row4_col1,#T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row4_col3{\n",
              "            color:  white;\n",
              "             background-color:  green;\n",
              "            width:  2em;\n",
              "            height:  2em;\n",
              "            text-align:  center;\n",
              "        }#T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row0_col2,#T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row0_col3,#T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row3_col0,#T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row3_col4,#T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row3_col5,#T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row4_col0,#T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row4_col4,#T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row4_col5,#T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row5_col0,#T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row5_col1,#T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row5_col2,#T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row5_col3,#T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row5_col4,#T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row5_col5{\n",
              "            color:  lightgrey;\n",
              "            width:  2em;\n",
              "            height:  2em;\n",
              "            text-align:  center;\n",
              "        }</style><table id=\"T_c16f0b14_4848_11eb_aa0b_0242ac1c0002\" ><thead>    <tr>        <th class=\"blank level0\" ></th>        <th class=\"col_heading level0 col0\" >0</th>        <th class=\"col_heading level0 col1\" >1</th>        <th class=\"col_heading level0 col2\" >2</th>        <th class=\"col_heading level0 col3\" >3</th>        <th class=\"col_heading level0 col4\" >4</th>        <th class=\"col_heading level0 col5\" >5</th>    </tr></thead><tbody>\n",
              "                <tr>\n",
              "                        <th id=\"T_c16f0b14_4848_11eb_aa0b_0242ac1c0002level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
              "                        <td id=\"T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row0_col0\" class=\"data row0 col0\" >-1</td>\n",
              "                        <td id=\"T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row0_col1\" class=\"data row0 col1\" >1</td>\n",
              "                        <td id=\"T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row0_col2\" class=\"data row0 col2\" >0</td>\n",
              "                        <td id=\"T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row0_col3\" class=\"data row0 col3\" >0</td>\n",
              "                        <td id=\"T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row0_col4\" class=\"data row0 col4\" >-2</td>\n",
              "                        <td id=\"T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row0_col5\" class=\"data row0 col5\" >2</td>\n",
              "            </tr>\n",
              "            <tr>\n",
              "                        <th id=\"T_c16f0b14_4848_11eb_aa0b_0242ac1c0002level0_row1\" class=\"row_heading level0 row1\" >1</th>\n",
              "                        <td id=\"T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row1_col0\" class=\"data row1 col0\" >3</td>\n",
              "                        <td id=\"T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row1_col1\" class=\"data row1 col1\" >-3</td>\n",
              "                        <td id=\"T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row1_col2\" class=\"data row1 col2\" >4</td>\n",
              "                        <td id=\"T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row1_col3\" class=\"data row1 col3\" >-4</td>\n",
              "                        <td id=\"T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row1_col4\" class=\"data row1 col4\" >5</td>\n",
              "                        <td id=\"T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row1_col5\" class=\"data row1 col5\" >-5</td>\n",
              "            </tr>\n",
              "            <tr>\n",
              "                        <th id=\"T_c16f0b14_4848_11eb_aa0b_0242ac1c0002level0_row2\" class=\"row_heading level0 row2\" >2</th>\n",
              "                        <td id=\"T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row2_col0\" class=\"data row2 col0\" >-6</td>\n",
              "                        <td id=\"T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row2_col1\" class=\"data row2 col1\" >6</td>\n",
              "                        <td id=\"T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row2_col2\" class=\"data row2 col2\" >-7</td>\n",
              "                        <td id=\"T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row2_col3\" class=\"data row2 col3\" >7</td>\n",
              "                        <td id=\"T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row2_col4\" class=\"data row2 col4\" >-8</td>\n",
              "                        <td id=\"T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row2_col5\" class=\"data row2 col5\" >8</td>\n",
              "            </tr>\n",
              "            <tr>\n",
              "                        <th id=\"T_c16f0b14_4848_11eb_aa0b_0242ac1c0002level0_row3\" class=\"row_heading level0 row3\" >3</th>\n",
              "                        <td id=\"T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row3_col0\" class=\"data row3 col0\" >0</td>\n",
              "                        <td id=\"T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row3_col1\" class=\"data row3 col1\" >-9</td>\n",
              "                        <td id=\"T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row3_col2\" class=\"data row3 col2\" >9</td>\n",
              "                        <td id=\"T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row3_col3\" class=\"data row3 col3\" >-10</td>\n",
              "                        <td id=\"T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row3_col4\" class=\"data row3 col4\" >0</td>\n",
              "                        <td id=\"T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row3_col5\" class=\"data row3 col5\" >0</td>\n",
              "            </tr>\n",
              "            <tr>\n",
              "                        <th id=\"T_c16f0b14_4848_11eb_aa0b_0242ac1c0002level0_row4\" class=\"row_heading level0 row4\" >4</th>\n",
              "                        <td id=\"T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row4_col0\" class=\"data row4 col0\" >0</td>\n",
              "                        <td id=\"T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row4_col1\" class=\"data row4 col1\" >10</td>\n",
              "                        <td id=\"T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row4_col2\" class=\"data row4 col2\" >-11</td>\n",
              "                        <td id=\"T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row4_col3\" class=\"data row4 col3\" >11</td>\n",
              "                        <td id=\"T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row4_col4\" class=\"data row4 col4\" >0</td>\n",
              "                        <td id=\"T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row4_col5\" class=\"data row4 col5\" >0</td>\n",
              "            </tr>\n",
              "            <tr>\n",
              "                        <th id=\"T_c16f0b14_4848_11eb_aa0b_0242ac1c0002level0_row5\" class=\"row_heading level0 row5\" >5</th>\n",
              "                        <td id=\"T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row5_col0\" class=\"data row5 col0\" >0</td>\n",
              "                        <td id=\"T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row5_col1\" class=\"data row5 col1\" >0</td>\n",
              "                        <td id=\"T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row5_col2\" class=\"data row5 col2\" >0</td>\n",
              "                        <td id=\"T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row5_col3\" class=\"data row5 col3\" >0</td>\n",
              "                        <td id=\"T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row5_col4\" class=\"data row5 col4\" >0</td>\n",
              "                        <td id=\"T_c16f0b14_4848_11eb_aa0b_0242ac1c0002row5_col5\" class=\"data row5 col5\" >0</td>\n",
              "            </tr>\n",
              "    </tbody></table>"
            ],
            "text/plain": [
              "<pandas.io.formats.style.Styler at 0x7ffaccb2def0>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 392
        },
        "id": "DsBI28ECWnwd",
        "outputId": "e5f4d825-ebcd-40c3-8ab9-3b5f8636f716"
      },
      "source": [
        "# complex matrix A with |det(A)| = #number_of_tilings\n",
        "Ac = A.copy().astype('object')\n",
        "Ac[Ac==complex(0,0)] = 0\n",
        "Ac[Ac==complex(1,0)] = 1\n",
        "Ac[Ac==complex(0,1)] = 'i'\n",
        "display(showMatrix(Ac))"
      ],
      "execution_count": 46,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
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              "            color:  white;\n",
              "             background-color:  black;\n",
              "            width:  2em;\n",
              "            height:  2em;\n",
              "            text-align:  center;\n",
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              "            color:  lightgrey;\n",
              "            width:  2em;\n",
              "            height:  2em;\n",
              "            text-align:  center;\n",
              "        }#T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row1_col4,#T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row2_col5,#T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row3_col2,#T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row3_col6,#T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row4_col1,#T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row4_col3,#T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row4_col7,#T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row5_col2,#T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row5_col6,#T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row5_col8,#T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row6_col3,#T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row6_col7,#T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row6_col9,#T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row7_col4,#T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row8_col9,#T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row9_col8,#T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row9_col10,#T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row10_col9{\n",
              "            color:  white;\n",
              "             background-color:  green;\n",
              "            width:  2em;\n",
              "            height:  2em;\n",
              "            text-align:  center;\n",
              "        }</style><table id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002\" ><thead>    <tr>        <th class=\"blank level0\" ></th>        <th class=\"col_heading level0 col0\" >0</th>        <th class=\"col_heading level0 col1\" >1</th>        <th class=\"col_heading level0 col2\" >2</th>        <th class=\"col_heading level0 col3\" >3</th>        <th class=\"col_heading level0 col4\" >4</th>        <th class=\"col_heading level0 col5\" >5</th>        <th class=\"col_heading level0 col6\" >6</th>        <th class=\"col_heading level0 col7\" >7</th>        <th class=\"col_heading level0 col8\" >8</th>        <th class=\"col_heading level0 col9\" >9</th>        <th class=\"col_heading level0 col10\" >10</th>    </tr></thead><tbody>\n",
              "                <tr>\n",
              "                        <th id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row0_col0\" class=\"data row0 col0\" >1</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row0_col1\" class=\"data row0 col1\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row0_col2\" class=\"data row0 col2\" >i</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row0_col3\" class=\"data row0 col3\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row0_col4\" class=\"data row0 col4\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row0_col5\" class=\"data row0 col5\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row0_col6\" class=\"data row0 col6\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row0_col7\" class=\"data row0 col7\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row0_col8\" class=\"data row0 col8\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row0_col9\" class=\"data row0 col9\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row0_col10\" class=\"data row0 col10\" >0</td>\n",
              "            </tr>\n",
              "            <tr>\n",
              "                        <th id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002level0_row1\" class=\"row_heading level0 row1\" >1</th>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row1_col0\" class=\"data row1 col0\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row1_col1\" class=\"data row1 col1\" >1</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row1_col2\" class=\"data row1 col2\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row1_col3\" class=\"data row1 col3\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row1_col4\" class=\"data row1 col4\" >i</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row1_col5\" class=\"data row1 col5\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row1_col6\" class=\"data row1 col6\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row1_col7\" class=\"data row1 col7\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row1_col8\" class=\"data row1 col8\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row1_col9\" class=\"data row1 col9\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row1_col10\" class=\"data row1 col10\" >0</td>\n",
              "            </tr>\n",
              "            <tr>\n",
              "                        <th id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002level0_row2\" class=\"row_heading level0 row2\" >2</th>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row2_col0\" class=\"data row2 col0\" >i</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row2_col1\" class=\"data row2 col1\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row2_col2\" class=\"data row2 col2\" >1</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row2_col3\" class=\"data row2 col3\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row2_col4\" class=\"data row2 col4\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row2_col5\" class=\"data row2 col5\" >i</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row2_col6\" class=\"data row2 col6\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row2_col7\" class=\"data row2 col7\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row2_col8\" class=\"data row2 col8\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row2_col9\" class=\"data row2 col9\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row2_col10\" class=\"data row2 col10\" >0</td>\n",
              "            </tr>\n",
              "            <tr>\n",
              "                        <th id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002level0_row3\" class=\"row_heading level0 row3\" >3</th>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row3_col0\" class=\"data row3 col0\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row3_col1\" class=\"data row3 col1\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row3_col2\" class=\"data row3 col2\" >1</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row3_col3\" class=\"data row3 col3\" >1</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row3_col4\" class=\"data row3 col4\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row3_col5\" class=\"data row3 col5\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row3_col6\" class=\"data row3 col6\" >i</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row3_col7\" class=\"data row3 col7\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row3_col8\" class=\"data row3 col8\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row3_col9\" class=\"data row3 col9\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row3_col10\" class=\"data row3 col10\" >0</td>\n",
              "            </tr>\n",
              "            <tr>\n",
              "                        <th id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002level0_row4\" class=\"row_heading level0 row4\" >4</th>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row4_col0\" class=\"data row4 col0\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row4_col1\" class=\"data row4 col1\" >i</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row4_col2\" class=\"data row4 col2\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row4_col3\" class=\"data row4 col3\" >1</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row4_col4\" class=\"data row4 col4\" >1</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row4_col5\" class=\"data row4 col5\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row4_col6\" class=\"data row4 col6\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row4_col7\" class=\"data row4 col7\" >i</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row4_col8\" class=\"data row4 col8\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row4_col9\" class=\"data row4 col9\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row4_col10\" class=\"data row4 col10\" >0</td>\n",
              "            </tr>\n",
              "            <tr>\n",
              "                        <th id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002level0_row5\" class=\"row_heading level0 row5\" >5</th>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row5_col0\" class=\"data row5 col0\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row5_col1\" class=\"data row5 col1\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row5_col2\" class=\"data row5 col2\" >i</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row5_col3\" class=\"data row5 col3\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row5_col4\" class=\"data row5 col4\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row5_col5\" class=\"data row5 col5\" >1</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row5_col6\" class=\"data row5 col6\" >1</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row5_col7\" class=\"data row5 col7\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row5_col8\" class=\"data row5 col8\" >i</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row5_col9\" class=\"data row5 col9\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row5_col10\" class=\"data row5 col10\" >0</td>\n",
              "            </tr>\n",
              "            <tr>\n",
              "                        <th id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002level0_row6\" class=\"row_heading level0 row6\" >6</th>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row6_col0\" class=\"data row6 col0\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row6_col1\" class=\"data row6 col1\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row6_col2\" class=\"data row6 col2\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row6_col3\" class=\"data row6 col3\" >i</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row6_col4\" class=\"data row6 col4\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row6_col5\" class=\"data row6 col5\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row6_col6\" class=\"data row6 col6\" >1</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row6_col7\" class=\"data row6 col7\" >1</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row6_col8\" class=\"data row6 col8\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row6_col9\" class=\"data row6 col9\" >i</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row6_col10\" class=\"data row6 col10\" >0</td>\n",
              "            </tr>\n",
              "            <tr>\n",
              "                        <th id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002level0_row7\" class=\"row_heading level0 row7\" >7</th>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row7_col0\" class=\"data row7 col0\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row7_col1\" class=\"data row7 col1\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row7_col2\" class=\"data row7 col2\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row7_col3\" class=\"data row7 col3\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row7_col4\" class=\"data row7 col4\" >i</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row7_col5\" class=\"data row7 col5\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row7_col6\" class=\"data row7 col6\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row7_col7\" class=\"data row7 col7\" >1</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row7_col8\" class=\"data row7 col8\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row7_col9\" class=\"data row7 col9\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row7_col10\" class=\"data row7 col10\" >0</td>\n",
              "            </tr>\n",
              "            <tr>\n",
              "                        <th id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002level0_row8\" class=\"row_heading level0 row8\" >8</th>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row8_col0\" class=\"data row8 col0\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row8_col1\" class=\"data row8 col1\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row8_col2\" class=\"data row8 col2\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row8_col3\" class=\"data row8 col3\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row8_col4\" class=\"data row8 col4\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row8_col5\" class=\"data row8 col5\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row8_col6\" class=\"data row8 col6\" >i</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row8_col7\" class=\"data row8 col7\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row8_col8\" class=\"data row8 col8\" >1</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row8_col9\" class=\"data row8 col9\" >1</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row8_col10\" class=\"data row8 col10\" >i</td>\n",
              "            </tr>\n",
              "            <tr>\n",
              "                        <th id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002level0_row9\" class=\"row_heading level0 row9\" >9</th>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row9_col0\" class=\"data row9 col0\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row9_col1\" class=\"data row9 col1\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row9_col2\" class=\"data row9 col2\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row9_col3\" class=\"data row9 col3\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row9_col4\" class=\"data row9 col4\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row9_col5\" class=\"data row9 col5\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row9_col6\" class=\"data row9 col6\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row9_col7\" class=\"data row9 col7\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row9_col8\" class=\"data row9 col8\" >i</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row9_col9\" class=\"data row9 col9\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row9_col10\" class=\"data row9 col10\" >1</td>\n",
              "            </tr>\n",
              "            <tr>\n",
              "                        <th id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002level0_row10\" class=\"row_heading level0 row10\" >10</th>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row10_col0\" class=\"data row10 col0\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row10_col1\" class=\"data row10 col1\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row10_col2\" class=\"data row10 col2\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row10_col3\" class=\"data row10 col3\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row10_col4\" class=\"data row10 col4\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row10_col5\" class=\"data row10 col5\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row10_col6\" class=\"data row10 col6\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row10_col7\" class=\"data row10 col7\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row10_col8\" class=\"data row10 col8\" >0</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row10_col9\" class=\"data row10 col9\" >i</td>\n",
              "                        <td id=\"T_c3ec2c46_4848_11eb_aa0b_0242ac1c0002row10_col10\" class=\"data row10 col10\" >1</td>\n",
              "            </tr>\n",
              "    </tbody></table>"
            ],
            "text/plain": [
              "<pandas.io.formats.style.Styler at 0x7ffaccb2d9e8>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "BidcQbrtWwm3",
        "outputId": "afab7b9a-04e8-4a33-db96-d79cf5a99037"
      },
      "source": [
        "print(f'\\nNumber of Tilings: {numberOfTilings(M)}')"
      ],
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "\n",
            "Number of Tilings: 88\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rzXrhNIHKiTV"
      },
      "source": [
        "# Number of tilings for the 'sunclasses'\n",
        "\n",
        "A more complex shape in the [video](https://www.youtube.com/watch?v=Yy7Q8IWNfHM&t=860s).\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 203
        },
        "id": "u-7RUFUA-GP-",
        "outputId": "dc5f9dad-6cbd-4b38-963d-45d50261720b"
      },
      "source": [
        "M = [[1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1],\n",
        "     [1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1],\n",
        "     [0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0],\n",
        "     [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0]]\n",
        "\n",
        "\n",
        "display(showMatrix(M))\n",
        "M = np.array(M)[::-1,:]\n",
        "print(f'\\nNumber of Tilings: {numberOfTilings(M)}')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
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              "            color:  lightgrey;\n",
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              "            height:  2em;\n",
              "            text-align:  center;\n",
              "        }</style><table id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002\" ><thead>    <tr>        <th class=\"blank level0\" ></th>        <th class=\"col_heading level0 col0\" >0</th>        <th class=\"col_heading level0 col1\" >1</th>        <th class=\"col_heading level0 col2\" >2</th>        <th class=\"col_heading level0 col3\" >3</th>        <th class=\"col_heading level0 col4\" >4</th>        <th class=\"col_heading level0 col5\" >5</th>        <th class=\"col_heading level0 col6\" >6</th>        <th class=\"col_heading level0 col7\" >7</th>        <th class=\"col_heading level0 col8\" >8</th>        <th class=\"col_heading level0 col9\" >9</th>        <th class=\"col_heading level0 col10\" >10</th>        <th class=\"col_heading level0 col11\" >11</th>        <th class=\"col_heading level0 col12\" >12</th>        <th class=\"col_heading level0 col13\" >13</th>        <th class=\"col_heading level0 col14\" >14</th>        <th class=\"col_heading level0 col15\" >15</th>        <th class=\"col_heading level0 col16\" >16</th>        <th class=\"col_heading level0 col17\" >17</th>    </tr></thead><tbody>\n",
              "                <tr>\n",
              "                        <th id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row0_col0\" class=\"data row0 col0\" >1</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row0_col1\" class=\"data row0 col1\" >1</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row0_col2\" class=\"data row0 col2\" >1</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row0_col3\" class=\"data row0 col3\" >0</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row0_col4\" class=\"data row0 col4\" >0</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row0_col5\" class=\"data row0 col5\" >1</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row0_col6\" class=\"data row0 col6\" >1</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row0_col7\" class=\"data row0 col7\" >1</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row0_col8\" class=\"data row0 col8\" >0</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row0_col9\" class=\"data row0 col9\" >0</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row0_col10\" class=\"data row0 col10\" >1</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row0_col11\" class=\"data row0 col11\" >1</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row0_col12\" class=\"data row0 col12\" >1</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row0_col13\" class=\"data row0 col13\" >0</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row0_col14\" class=\"data row0 col14\" >0</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row0_col15\" class=\"data row0 col15\" >1</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row0_col16\" class=\"data row0 col16\" >1</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row0_col17\" class=\"data row0 col17\" >1</td>\n",
              "            </tr>\n",
              "            <tr>\n",
              "                        <th id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002level0_row1\" class=\"row_heading level0 row1\" >1</th>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row1_col0\" class=\"data row1 col0\" >1</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row1_col1\" class=\"data row1 col1\" >1</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row1_col2\" class=\"data row1 col2\" >1</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row1_col3\" class=\"data row1 col3\" >1</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row1_col4\" class=\"data row1 col4\" >1</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row1_col5\" class=\"data row1 col5\" >1</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row1_col6\" class=\"data row1 col6\" >0</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row1_col7\" class=\"data row1 col7\" >1</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row1_col8\" class=\"data row1 col8\" >1</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row1_col9\" class=\"data row1 col9\" >1</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row1_col10\" class=\"data row1 col10\" >1</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row1_col11\" class=\"data row1 col11\" >0</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row1_col12\" class=\"data row1 col12\" >1</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row1_col13\" class=\"data row1 col13\" >1</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row1_col14\" class=\"data row1 col14\" >1</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row1_col15\" class=\"data row1 col15\" >1</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row1_col16\" class=\"data row1 col16\" >1</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row1_col17\" class=\"data row1 col17\" >1</td>\n",
              "            </tr>\n",
              "            <tr>\n",
              "                        <th id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002level0_row2\" class=\"row_heading level0 row2\" >2</th>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row2_col0\" class=\"data row2 col0\" >0</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row2_col1\" class=\"data row2 col1\" >0</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row2_col2\" class=\"data row2 col2\" >0</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row2_col3\" class=\"data row2 col3\" >1</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row2_col4\" class=\"data row2 col4\" >1</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row2_col5\" class=\"data row2 col5\" >1</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row2_col6\" class=\"data row2 col6\" >0</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row2_col7\" class=\"data row2 col7\" >1</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row2_col8\" class=\"data row2 col8\" >1</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row2_col9\" class=\"data row2 col9\" >1</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row2_col10\" class=\"data row2 col10\" >1</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row2_col11\" class=\"data row2 col11\" >0</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row2_col12\" class=\"data row2 col12\" >1</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row2_col13\" class=\"data row2 col13\" >1</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row2_col14\" class=\"data row2 col14\" >1</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row2_col15\" class=\"data row2 col15\" >0</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row2_col16\" class=\"data row2 col16\" >0</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row2_col17\" class=\"data row2 col17\" >0</td>\n",
              "            </tr>\n",
              "            <tr>\n",
              "                        <th id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002level0_row3\" class=\"row_heading level0 row3\" >3</th>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row3_col0\" class=\"data row3 col0\" >0</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row3_col1\" class=\"data row3 col1\" >0</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row3_col2\" class=\"data row3 col2\" >0</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row3_col3\" class=\"data row3 col3\" >0</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row3_col4\" class=\"data row3 col4\" >0</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row3_col5\" class=\"data row3 col5\" >1</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row3_col6\" class=\"data row3 col6\" >1</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row3_col7\" class=\"data row3 col7\" >1</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row3_col8\" class=\"data row3 col8\" >0</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row3_col9\" class=\"data row3 col9\" >0</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row3_col10\" class=\"data row3 col10\" >1</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row3_col11\" class=\"data row3 col11\" >1</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row3_col12\" class=\"data row3 col12\" >1</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row3_col13\" class=\"data row3 col13\" >0</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row3_col14\" class=\"data row3 col14\" >0</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row3_col15\" class=\"data row3 col15\" >0</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row3_col16\" class=\"data row3 col16\" >0</td>\n",
              "                        <td id=\"T_16d9f71c_4844_11eb_aa0b_0242ac1c0002row3_col17\" class=\"data row3 col17\" >0</td>\n",
              "            </tr>\n",
              "    </tbody></table>"
            ],
            "text/plain": [
              "<pandas.io.formats.style.Styler at 0x7ffad701ef98>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "\n",
            "Number of Tilings: 666\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gdnZ-C4FSnxh"
      },
      "source": [
        "## Space Invader shape"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 299
        },
        "id": "-xMk0PmzfEF9",
        "outputId": "b2650382-af27-47c2-e826-be4cdf6dc5ed"
      },
      "source": [
        "M = [[0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0],\n",
        "     [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0],\n",
        "     [1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1],\n",
        "     [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n",
        "     [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0],\n",
        "     [0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0],\n",
        "     [0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0],\n",
        "     ]\n",
        "\n",
        "display(showMatrix(M))\n",
        "M = np.array(M)[::-1,:]\n",
        "print(f'\\nNumber of Tilings: {numberOfTilings(M)}')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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              "            text-align:  center;\n",
              "        }#T_16ee8740_4844_11eb_aa0b_0242ac1c0002row0_col3,#T_16ee8740_4844_11eb_aa0b_0242ac1c0002row0_col5,#T_16ee8740_4844_11eb_aa0b_0242ac1c0002row0_col7,#T_16ee8740_4844_11eb_aa0b_0242ac1c0002row1_col2,#T_16ee8740_4844_11eb_aa0b_0242ac1c0002row1_col4,#T_16ee8740_4844_11eb_aa0b_0242ac1c0002row1_col6,#T_16ee8740_4844_11eb_aa0b_0242ac1c0002row1_col8,#T_16ee8740_4844_11eb_aa0b_0242ac1c0002row1_col10,#T_16ee8740_4844_11eb_aa0b_0242ac1c0002row2_col1,#T_16ee8740_4844_11eb_aa0b_0242ac1c0002row2_col5,#T_16ee8740_4844_11eb_aa0b_0242ac1c0002row2_col9,#T_16ee8740_4844_11eb_aa0b_0242ac1c0002row2_col11,#T_16ee8740_4844_11eb_aa0b_0242ac1c0002row3_col0,#T_16ee8740_4844_11eb_aa0b_0242ac1c0002row3_col2,#T_16ee8740_4844_11eb_aa0b_0242ac1c0002row3_col4,#T_16ee8740_4844_11eb_aa0b_0242ac1c0002row3_col6,#T_16ee8740_4844_11eb_aa0b_0242ac1c0002row3_col8,#T_16ee8740_4844_11eb_aa0b_0242ac1c0002row3_col10,#T_16ee8740_4844_11eb_aa0b_0242ac1c0002row4_col3,#T_16ee8740_4844_11eb_aa0b_0242ac1c0002row4_col5,#T_16ee8740_4844_11eb_aa0b_0242ac1c0002row4_col7,#T_16ee8740_4844_11eb_aa0b_0242ac1c0002row4_col9,#T_16ee8740_4844_11eb_aa0b_0242ac1c0002row5_col2,#T_16ee8740_4844_11eb_aa0b_0242ac1c0002row5_col6,#T_16ee8740_4844_11eb_aa0b_0242ac1c0002row5_col10,#T_16ee8740_4844_11eb_aa0b_0242ac1c0002row6_col3,#T_16ee8740_4844_11eb_aa0b_0242ac1c0002row6_col9{\n",
              "            color:  white;\n",
              "             background-color:  green;\n",
              "            width:  2em;\n",
              "            height:  2em;\n",
              "            text-align:  center;\n",
              "        }#T_16ee8740_4844_11eb_aa0b_0242ac1c0002row0_col4,#T_16ee8740_4844_11eb_aa0b_0242ac1c0002row0_col6,#T_16ee8740_4844_11eb_aa0b_0242ac1c0002row0_col8,#T_16ee8740_4844_11eb_aa0b_0242ac1c0002row1_col1,#T_16ee8740_4844_11eb_aa0b_0242ac1c0002row1_col3,#T_16ee8740_4844_11eb_aa0b_0242ac1c0002row1_col5,#T_16ee8740_4844_11eb_aa0b_0242ac1c0002row1_col7,#T_16ee8740_4844_11eb_aa0b_0242ac1c0002row1_col9,#T_16ee8740_4844_11eb_aa0b_0242ac1c0002row2_col0,#T_16ee8740_4844_11eb_aa0b_0242ac1c0002row2_col2,#T_16ee8740_4844_11eb_aa0b_0242ac1c0002row2_col6,#T_16ee8740_4844_11eb_aa0b_0242ac1c0002row2_col10,#T_16ee8740_4844_11eb_aa0b_0242ac1c0002row3_col1,#T_16ee8740_4844_11eb_aa0b_0242ac1c0002row3_col3,#T_16ee8740_4844_11eb_aa0b_0242ac1c0002row3_col5,#T_16ee8740_4844_11eb_aa0b_0242ac1c0002row3_col7,#T_16ee8740_4844_11eb_aa0b_0242ac1c0002row3_col9,#T_16ee8740_4844_11eb_aa0b_0242ac1c0002row3_col11,#T_16ee8740_4844_11eb_aa0b_0242ac1c0002row4_col2,#T_16ee8740_4844_11eb_aa0b_0242ac1c0002row4_col4,#T_16ee8740_4844_11eb_aa0b_0242ac1c0002row4_col6,#T_16ee8740_4844_11eb_aa0b_0242ac1c0002row4_col8,#T_16ee8740_4844_11eb_aa0b_0242ac1c0002row5_col1,#T_16ee8740_4844_11eb_aa0b_0242ac1c0002row5_col5,#T_16ee8740_4844_11eb_aa0b_0242ac1c0002row5_col9,#T_16ee8740_4844_11eb_aa0b_0242ac1c0002row6_col2,#T_16ee8740_4844_11eb_aa0b_0242ac1c0002row6_col8{\n",
              "            color:  white;\n",
              "             background-color:  black;\n",
              "            width:  2em;\n",
              "            height:  2em;\n",
              "            text-align:  center;\n",
              "        }</style><table id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002\" ><thead>    <tr>        <th class=\"blank level0\" ></th>        <th class=\"col_heading level0 col0\" >0</th>        <th class=\"col_heading level0 col1\" >1</th>        <th class=\"col_heading level0 col2\" >2</th>        <th class=\"col_heading level0 col3\" >3</th>        <th class=\"col_heading level0 col4\" >4</th>        <th class=\"col_heading level0 col5\" >5</th>        <th class=\"col_heading level0 col6\" >6</th>        <th class=\"col_heading level0 col7\" >7</th>        <th class=\"col_heading level0 col8\" >8</th>        <th class=\"col_heading level0 col9\" >9</th>        <th class=\"col_heading level0 col10\" >10</th>        <th class=\"col_heading level0 col11\" >11</th>    </tr></thead><tbody>\n",
              "                <tr>\n",
              "                        <th id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row0_col0\" class=\"data row0 col0\" >0</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row0_col1\" class=\"data row0 col1\" >0</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row0_col2\" class=\"data row0 col2\" >0</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row0_col3\" class=\"data row0 col3\" >1</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row0_col4\" class=\"data row0 col4\" >1</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row0_col5\" class=\"data row0 col5\" >1</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row0_col6\" class=\"data row0 col6\" >1</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row0_col7\" class=\"data row0 col7\" >1</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row0_col8\" class=\"data row0 col8\" >1</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row0_col9\" class=\"data row0 col9\" >0</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row0_col10\" class=\"data row0 col10\" >0</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row0_col11\" class=\"data row0 col11\" >0</td>\n",
              "            </tr>\n",
              "            <tr>\n",
              "                        <th id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002level0_row1\" class=\"row_heading level0 row1\" >1</th>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row1_col0\" class=\"data row1 col0\" >0</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row1_col1\" class=\"data row1 col1\" >1</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row1_col2\" class=\"data row1 col2\" >1</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row1_col3\" class=\"data row1 col3\" >1</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row1_col4\" class=\"data row1 col4\" >1</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row1_col5\" class=\"data row1 col5\" >1</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row1_col6\" class=\"data row1 col6\" >1</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row1_col7\" class=\"data row1 col7\" >1</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row1_col8\" class=\"data row1 col8\" >1</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row1_col9\" class=\"data row1 col9\" >1</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row1_col10\" class=\"data row1 col10\" >1</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row1_col11\" class=\"data row1 col11\" >0</td>\n",
              "            </tr>\n",
              "            <tr>\n",
              "                        <th id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002level0_row2\" class=\"row_heading level0 row2\" >2</th>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row2_col0\" class=\"data row2 col0\" >1</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row2_col1\" class=\"data row2 col1\" >1</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row2_col2\" class=\"data row2 col2\" >1</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row2_col3\" class=\"data row2 col3\" >0</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row2_col4\" class=\"data row2 col4\" >0</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row2_col5\" class=\"data row2 col5\" >1</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row2_col6\" class=\"data row2 col6\" >1</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row2_col7\" class=\"data row2 col7\" >0</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row2_col8\" class=\"data row2 col8\" >0</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row2_col9\" class=\"data row2 col9\" >1</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row2_col10\" class=\"data row2 col10\" >1</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row2_col11\" class=\"data row2 col11\" >1</td>\n",
              "            </tr>\n",
              "            <tr>\n",
              "                        <th id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002level0_row3\" class=\"row_heading level0 row3\" >3</th>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row3_col0\" class=\"data row3 col0\" >1</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row3_col1\" class=\"data row3 col1\" >1</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row3_col2\" class=\"data row3 col2\" >1</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row3_col3\" class=\"data row3 col3\" >1</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row3_col4\" class=\"data row3 col4\" >1</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row3_col5\" class=\"data row3 col5\" >1</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row3_col6\" class=\"data row3 col6\" >1</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row3_col7\" class=\"data row3 col7\" >1</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row3_col8\" class=\"data row3 col8\" >1</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row3_col9\" class=\"data row3 col9\" >1</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row3_col10\" class=\"data row3 col10\" >1</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row3_col11\" class=\"data row3 col11\" >1</td>\n",
              "            </tr>\n",
              "            <tr>\n",
              "                        <th id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002level0_row4\" class=\"row_heading level0 row4\" >4</th>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row4_col0\" class=\"data row4 col0\" >0</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row4_col1\" class=\"data row4 col1\" >0</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row4_col2\" class=\"data row4 col2\" >1</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row4_col3\" class=\"data row4 col3\" >1</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row4_col4\" class=\"data row4 col4\" >1</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row4_col5\" class=\"data row4 col5\" >1</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row4_col6\" class=\"data row4 col6\" >1</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row4_col7\" class=\"data row4 col7\" >1</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row4_col8\" class=\"data row4 col8\" >1</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row4_col9\" class=\"data row4 col9\" >1</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row4_col10\" class=\"data row4 col10\" >0</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row4_col11\" class=\"data row4 col11\" >0</td>\n",
              "            </tr>\n",
              "            <tr>\n",
              "                        <th id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002level0_row5\" class=\"row_heading level0 row5\" >5</th>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row5_col0\" class=\"data row5 col0\" >0</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row5_col1\" class=\"data row5 col1\" >1</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row5_col2\" class=\"data row5 col2\" >1</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row5_col3\" class=\"data row5 col3\" >0</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row5_col4\" class=\"data row5 col4\" >0</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row5_col5\" class=\"data row5 col5\" >1</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row5_col6\" class=\"data row5 col6\" >1</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row5_col7\" class=\"data row5 col7\" >0</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row5_col8\" class=\"data row5 col8\" >0</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row5_col9\" class=\"data row5 col9\" >1</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row5_col10\" class=\"data row5 col10\" >1</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row5_col11\" class=\"data row5 col11\" >0</td>\n",
              "            </tr>\n",
              "            <tr>\n",
              "                        <th id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002level0_row6\" class=\"row_heading level0 row6\" >6</th>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row6_col0\" class=\"data row6 col0\" >0</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row6_col1\" class=\"data row6 col1\" >0</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row6_col2\" class=\"data row6 col2\" >1</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row6_col3\" class=\"data row6 col3\" >1</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row6_col4\" class=\"data row6 col4\" >0</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row6_col5\" class=\"data row6 col5\" >0</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row6_col6\" class=\"data row6 col6\" >0</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row6_col7\" class=\"data row6 col7\" >0</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row6_col8\" class=\"data row6 col8\" >1</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row6_col9\" class=\"data row6 col9\" >1</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row6_col10\" class=\"data row6 col10\" >0</td>\n",
              "                        <td id=\"T_16ee8740_4844_11eb_aa0b_0242ac1c0002row6_col11\" class=\"data row6 col11\" >0</td>\n",
              "            </tr>\n",
              "    </tbody></table>"
            ],
            "text/plain": [
              "<pandas.io.formats.style.Styler at 0x7ffad701e4e0>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "\n",
            "Number of Tilings: 480\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7X58jxvpUVFf"
      },
      "source": [
        "# Grids of shape ($2\\times n$)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Xo9zqArIUc35",
        "outputId": "55a30f05-511b-4736-f2ec-20bf1393f409"
      },
      "source": [
        "for n in range(2,13):\n",
        "  print(f'n={n}: {numberOfTilings(np.ones((2,n)))} tilings')"
      ],
      "execution_count": 43,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "n=2: 2 tilings\n",
            "n=3: 3 tilings\n",
            "n=4: 5 tilings\n",
            "n=5: 8 tilings\n",
            "n=6: 13 tilings\n",
            "n=7: 21 tilings\n",
            "n=8: 34 tilings\n",
            "n=9: 55 tilings\n",
            "n=10: 89 tilings\n",
            "n=11: 144 tilings\n",
            "n=12: 233 tilings\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bRkS9QEhKmg7"
      },
      "source": [
        "# Number of tilings for an Aztec Diamond\n",
        "\n",
        "Function definition for generating Aztec Diamonds as in the video at [26:00](https://www.youtube.com/watch?v=Yy7Q8IWNfHM&t=1560s).\n",
        "\n",
        "This code block also demonstrates that the number of tiling for an Aztec Diamong **A(n)** equals $2^{1+2+3+...+n}$."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 412
        },
        "id": "SCEp8Huf3svt",
        "outputId": "1a5cd0aa-a68d-4167-c187-5c5204874b66"
      },
      "source": [
        "def AztecDiamond(n):\n",
        "  M = np.triu(np.ones((n,n), dtype=int))\n",
        "  M = np.concatenate((M[::-1,:], M))\n",
        "  return np.concatenate((M, M[:,::-1]), axis=1)\n",
        "\n",
        "# size of Aztec Diamong, note. the process slows down with n>7\n",
        "n = 5\n",
        "M=AztecDiamond(n)\n",
        "display(showMatrix(M))\n",
        "\n",
        "M = np.array(M)[::-1,:]\n",
        "print(f'\\nNumber of Tilings: {numberOfTilings(M)}\\n2^(1+2+..+n): {2**(n*(n+1)//2)}')\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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              "            color:  white;\n",
              "             background-color:  green;\n",
              "            width:  2em;\n",
              "            height:  2em;\n",
              "            text-align:  center;\n",
              "        }</style><table id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002\" ><thead>    <tr>        <th class=\"blank level0\" ></th>        <th class=\"col_heading level0 col0\" >0</th>        <th class=\"col_heading level0 col1\" >1</th>        <th class=\"col_heading level0 col2\" >2</th>        <th class=\"col_heading level0 col3\" >3</th>        <th class=\"col_heading level0 col4\" >4</th>        <th class=\"col_heading level0 col5\" >5</th>        <th class=\"col_heading level0 col6\" >6</th>        <th class=\"col_heading level0 col7\" >7</th>        <th class=\"col_heading level0 col8\" >8</th>        <th class=\"col_heading level0 col9\" >9</th>    </tr></thead><tbody>\n",
              "                <tr>\n",
              "                        <th id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row0_col0\" class=\"data row0 col0\" >0</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row0_col1\" class=\"data row0 col1\" >0</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row0_col2\" class=\"data row0 col2\" >0</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row0_col3\" class=\"data row0 col3\" >0</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row0_col4\" class=\"data row0 col4\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row0_col5\" class=\"data row0 col5\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row0_col6\" class=\"data row0 col6\" >0</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row0_col7\" class=\"data row0 col7\" >0</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row0_col8\" class=\"data row0 col8\" >0</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row0_col9\" class=\"data row0 col9\" >0</td>\n",
              "            </tr>\n",
              "            <tr>\n",
              "                        <th id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002level0_row1\" class=\"row_heading level0 row1\" >1</th>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row1_col0\" class=\"data row1 col0\" >0</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row1_col1\" class=\"data row1 col1\" >0</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row1_col2\" class=\"data row1 col2\" >0</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row1_col3\" class=\"data row1 col3\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row1_col4\" class=\"data row1 col4\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row1_col5\" class=\"data row1 col5\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row1_col6\" class=\"data row1 col6\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row1_col7\" class=\"data row1 col7\" >0</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row1_col8\" class=\"data row1 col8\" >0</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row1_col9\" class=\"data row1 col9\" >0</td>\n",
              "            </tr>\n",
              "            <tr>\n",
              "                        <th id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002level0_row2\" class=\"row_heading level0 row2\" >2</th>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row2_col0\" class=\"data row2 col0\" >0</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row2_col1\" class=\"data row2 col1\" >0</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row2_col2\" class=\"data row2 col2\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row2_col3\" class=\"data row2 col3\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row2_col4\" class=\"data row2 col4\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row2_col5\" class=\"data row2 col5\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row2_col6\" class=\"data row2 col6\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row2_col7\" class=\"data row2 col7\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row2_col8\" class=\"data row2 col8\" >0</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row2_col9\" class=\"data row2 col9\" >0</td>\n",
              "            </tr>\n",
              "            <tr>\n",
              "                        <th id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002level0_row3\" class=\"row_heading level0 row3\" >3</th>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row3_col0\" class=\"data row3 col0\" >0</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row3_col1\" class=\"data row3 col1\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row3_col2\" class=\"data row3 col2\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row3_col3\" class=\"data row3 col3\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row3_col4\" class=\"data row3 col4\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row3_col5\" class=\"data row3 col5\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row3_col6\" class=\"data row3 col6\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row3_col7\" class=\"data row3 col7\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row3_col8\" class=\"data row3 col8\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row3_col9\" class=\"data row3 col9\" >0</td>\n",
              "            </tr>\n",
              "            <tr>\n",
              "                        <th id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002level0_row4\" class=\"row_heading level0 row4\" >4</th>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row4_col0\" class=\"data row4 col0\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row4_col1\" class=\"data row4 col1\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row4_col2\" class=\"data row4 col2\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row4_col3\" class=\"data row4 col3\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row4_col4\" class=\"data row4 col4\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row4_col5\" class=\"data row4 col5\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row4_col6\" class=\"data row4 col6\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row4_col7\" class=\"data row4 col7\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row4_col8\" class=\"data row4 col8\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row4_col9\" class=\"data row4 col9\" >1</td>\n",
              "            </tr>\n",
              "            <tr>\n",
              "                        <th id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002level0_row5\" class=\"row_heading level0 row5\" >5</th>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row5_col0\" class=\"data row5 col0\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row5_col1\" class=\"data row5 col1\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row5_col2\" class=\"data row5 col2\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row5_col3\" class=\"data row5 col3\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row5_col4\" class=\"data row5 col4\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row5_col5\" class=\"data row5 col5\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row5_col6\" class=\"data row5 col6\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row5_col7\" class=\"data row5 col7\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row5_col8\" class=\"data row5 col8\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row5_col9\" class=\"data row5 col9\" >1</td>\n",
              "            </tr>\n",
              "            <tr>\n",
              "                        <th id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002level0_row6\" class=\"row_heading level0 row6\" >6</th>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row6_col0\" class=\"data row6 col0\" >0</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row6_col1\" class=\"data row6 col1\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row6_col2\" class=\"data row6 col2\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row6_col3\" class=\"data row6 col3\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row6_col4\" class=\"data row6 col4\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row6_col5\" class=\"data row6 col5\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row6_col6\" class=\"data row6 col6\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row6_col7\" class=\"data row6 col7\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row6_col8\" class=\"data row6 col8\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row6_col9\" class=\"data row6 col9\" >0</td>\n",
              "            </tr>\n",
              "            <tr>\n",
              "                        <th id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002level0_row7\" class=\"row_heading level0 row7\" >7</th>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row7_col0\" class=\"data row7 col0\" >0</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row7_col1\" class=\"data row7 col1\" >0</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row7_col2\" class=\"data row7 col2\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row7_col3\" class=\"data row7 col3\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row7_col4\" class=\"data row7 col4\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row7_col5\" class=\"data row7 col5\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row7_col6\" class=\"data row7 col6\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row7_col7\" class=\"data row7 col7\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row7_col8\" class=\"data row7 col8\" >0</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row7_col9\" class=\"data row7 col9\" >0</td>\n",
              "            </tr>\n",
              "            <tr>\n",
              "                        <th id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002level0_row8\" class=\"row_heading level0 row8\" >8</th>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row8_col0\" class=\"data row8 col0\" >0</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row8_col1\" class=\"data row8 col1\" >0</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row8_col2\" class=\"data row8 col2\" >0</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row8_col3\" class=\"data row8 col3\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row8_col4\" class=\"data row8 col4\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row8_col5\" class=\"data row8 col5\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row8_col6\" class=\"data row8 col6\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row8_col7\" class=\"data row8 col7\" >0</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row8_col8\" class=\"data row8 col8\" >0</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row8_col9\" class=\"data row8 col9\" >0</td>\n",
              "            </tr>\n",
              "            <tr>\n",
              "                        <th id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002level0_row9\" class=\"row_heading level0 row9\" >9</th>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row9_col0\" class=\"data row9 col0\" >0</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row9_col1\" class=\"data row9 col1\" >0</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row9_col2\" class=\"data row9 col2\" >0</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row9_col3\" class=\"data row9 col3\" >0</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row9_col4\" class=\"data row9 col4\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row9_col5\" class=\"data row9 col5\" >1</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row9_col6\" class=\"data row9 col6\" >0</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row9_col7\" class=\"data row9 col7\" >0</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row9_col8\" class=\"data row9 col8\" >0</td>\n",
              "                        <td id=\"T_16fea65c_4844_11eb_aa0b_0242ac1c0002row9_col9\" class=\"data row9 col9\" >0</td>\n",
              "            </tr>\n",
              "    </tbody></table>"
            ],
            "text/plain": [
              "<pandas.io.formats.style.Styler at 0x7ffad6fd0630>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "\n",
            "Number of Tilings: 32768\n",
            "2^(1+2+..+n): 32768\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QraBTuw0POt-",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "79de5eeb-daaa-4c44-b2c2-77312892355d"
      },
      "source": [
        "A,B,N = calculateMatrix(M)\n",
        "print(f'Number of tilings: {numberOfTilings(M)}')\n",
        "display(showMatrix(N))\n",
        "A,B"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Number of tilings: 32768\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
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              "            color:  white;\n",
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              "            text-align:  center;\n",
              "        }</style><table id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002\" ><thead>    <tr>        <th class=\"blank level0\" ></th>        <th class=\"col_heading level0 col0\" >0</th>        <th class=\"col_heading level0 col1\" >1</th>        <th class=\"col_heading level0 col2\" >2</th>        <th class=\"col_heading level0 col3\" >3</th>        <th class=\"col_heading level0 col4\" >4</th>        <th class=\"col_heading level0 col5\" >5</th>        <th class=\"col_heading level0 col6\" >6</th>        <th class=\"col_heading level0 col7\" >7</th>        <th class=\"col_heading level0 col8\" >8</th>        <th class=\"col_heading level0 col9\" >9</th>    </tr></thead><tbody>\n",
              "                <tr>\n",
              "                        <th id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row0_col0\" class=\"data row0 col0\" >0</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row0_col1\" class=\"data row0 col1\" >0</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row0_col2\" class=\"data row0 col2\" >0</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row0_col3\" class=\"data row0 col3\" >0</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row0_col4\" class=\"data row0 col4\" >-1</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row0_col5\" class=\"data row0 col5\" >1</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row0_col6\" class=\"data row0 col6\" >0</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row0_col7\" class=\"data row0 col7\" >0</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row0_col8\" class=\"data row0 col8\" >0</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row0_col9\" class=\"data row0 col9\" >0</td>\n",
              "            </tr>\n",
              "            <tr>\n",
              "                        <th id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002level0_row1\" class=\"row_heading level0 row1\" >1</th>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row1_col0\" class=\"data row1 col0\" >0</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row1_col1\" class=\"data row1 col1\" >0</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row1_col2\" class=\"data row1 col2\" >0</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row1_col3\" class=\"data row1 col3\" >-2</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row1_col4\" class=\"data row1 col4\" >2</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row1_col5\" class=\"data row1 col5\" >-3</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row1_col6\" class=\"data row1 col6\" >3</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row1_col7\" class=\"data row1 col7\" >0</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row1_col8\" class=\"data row1 col8\" >0</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row1_col9\" class=\"data row1 col9\" >0</td>\n",
              "            </tr>\n",
              "            <tr>\n",
              "                        <th id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002level0_row2\" class=\"row_heading level0 row2\" >2</th>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row2_col0\" class=\"data row2 col0\" >0</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row2_col1\" class=\"data row2 col1\" >0</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row2_col2\" class=\"data row2 col2\" >-4</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row2_col3\" class=\"data row2 col3\" >4</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row2_col4\" class=\"data row2 col4\" >-5</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row2_col5\" class=\"data row2 col5\" >5</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row2_col6\" class=\"data row2 col6\" >-6</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row2_col7\" class=\"data row2 col7\" >6</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row2_col8\" class=\"data row2 col8\" >0</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row2_col9\" class=\"data row2 col9\" >0</td>\n",
              "            </tr>\n",
              "            <tr>\n",
              "                        <th id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002level0_row3\" class=\"row_heading level0 row3\" >3</th>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row3_col0\" class=\"data row3 col0\" >0</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row3_col1\" class=\"data row3 col1\" >-7</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row3_col2\" class=\"data row3 col2\" >7</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row3_col3\" class=\"data row3 col3\" >-8</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row3_col4\" class=\"data row3 col4\" >8</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row3_col5\" class=\"data row3 col5\" >-9</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row3_col6\" class=\"data row3 col6\" >9</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row3_col7\" class=\"data row3 col7\" >-10</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row3_col8\" class=\"data row3 col8\" >10</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row3_col9\" class=\"data row3 col9\" >0</td>\n",
              "            </tr>\n",
              "            <tr>\n",
              "                        <th id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002level0_row4\" class=\"row_heading level0 row4\" >4</th>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row4_col0\" class=\"data row4 col0\" >-11</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row4_col1\" class=\"data row4 col1\" >11</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row4_col2\" class=\"data row4 col2\" >-12</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row4_col3\" class=\"data row4 col3\" >12</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row4_col4\" class=\"data row4 col4\" >-13</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row4_col5\" class=\"data row4 col5\" >13</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row4_col6\" class=\"data row4 col6\" >-14</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row4_col7\" class=\"data row4 col7\" >14</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row4_col8\" class=\"data row4 col8\" >-15</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row4_col9\" class=\"data row4 col9\" >15</td>\n",
              "            </tr>\n",
              "            <tr>\n",
              "                        <th id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002level0_row5\" class=\"row_heading level0 row5\" >5</th>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row5_col0\" class=\"data row5 col0\" >16</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row5_col1\" class=\"data row5 col1\" >-16</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row5_col2\" class=\"data row5 col2\" >17</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row5_col3\" class=\"data row5 col3\" >-17</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row5_col4\" class=\"data row5 col4\" >18</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row5_col5\" class=\"data row5 col5\" >-18</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row5_col6\" class=\"data row5 col6\" >19</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row5_col7\" class=\"data row5 col7\" >-19</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row5_col8\" class=\"data row5 col8\" >20</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row5_col9\" class=\"data row5 col9\" >-20</td>\n",
              "            </tr>\n",
              "            <tr>\n",
              "                        <th id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002level0_row6\" class=\"row_heading level0 row6\" >6</th>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row6_col0\" class=\"data row6 col0\" >0</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row6_col1\" class=\"data row6 col1\" >21</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row6_col2\" class=\"data row6 col2\" >-21</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row6_col3\" class=\"data row6 col3\" >22</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row6_col4\" class=\"data row6 col4\" >-22</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row6_col5\" class=\"data row6 col5\" >23</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row6_col6\" class=\"data row6 col6\" >-23</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row6_col7\" class=\"data row6 col7\" >24</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row6_col8\" class=\"data row6 col8\" >-24</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row6_col9\" class=\"data row6 col9\" >0</td>\n",
              "            </tr>\n",
              "            <tr>\n",
              "                        <th id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002level0_row7\" class=\"row_heading level0 row7\" >7</th>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row7_col0\" class=\"data row7 col0\" >0</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row7_col1\" class=\"data row7 col1\" >0</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row7_col2\" class=\"data row7 col2\" >25</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row7_col3\" class=\"data row7 col3\" >-25</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row7_col4\" class=\"data row7 col4\" >26</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row7_col5\" class=\"data row7 col5\" >-26</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row7_col6\" class=\"data row7 col6\" >27</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row7_col7\" class=\"data row7 col7\" >-27</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row7_col8\" class=\"data row7 col8\" >0</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row7_col9\" class=\"data row7 col9\" >0</td>\n",
              "            </tr>\n",
              "            <tr>\n",
              "                        <th id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002level0_row8\" class=\"row_heading level0 row8\" >8</th>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row8_col0\" class=\"data row8 col0\" >0</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row8_col1\" class=\"data row8 col1\" >0</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row8_col2\" class=\"data row8 col2\" >0</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row8_col3\" class=\"data row8 col3\" >28</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row8_col4\" class=\"data row8 col4\" >-28</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row8_col5\" class=\"data row8 col5\" >29</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row8_col6\" class=\"data row8 col6\" >-29</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row8_col7\" class=\"data row8 col7\" >0</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row8_col8\" class=\"data row8 col8\" >0</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row8_col9\" class=\"data row8 col9\" >0</td>\n",
              "            </tr>\n",
              "            <tr>\n",
              "                        <th id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002level0_row9\" class=\"row_heading level0 row9\" >9</th>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row9_col0\" class=\"data row9 col0\" >0</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row9_col1\" class=\"data row9 col1\" >0</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row9_col2\" class=\"data row9 col2\" >0</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row9_col3\" class=\"data row9 col3\" >0</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row9_col4\" class=\"data row9 col4\" >30</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row9_col5\" class=\"data row9 col5\" >-30</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row9_col6\" class=\"data row9 col6\" >0</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row9_col7\" class=\"data row9 col7\" >0</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row9_col8\" class=\"data row9 col8\" >0</td>\n",
              "                        <td id=\"T_170d7f7e_4844_11eb_aa0b_0242ac1c0002row9_col9\" class=\"data row9 col9\" >0</td>\n",
              "            </tr>\n",
              "    </tbody></table>"
            ],
            "text/plain": [
              "<pandas.io.formats.style.Styler at 0x7ffad892b898>"
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          },
          "metadata": {
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        {
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              "         0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+1.j,\n",
              "         0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j,\n",
              "         0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n",
              "        [0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j,\n",
              "         0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j,\n",
              "         0.+1.j, 0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j, 1.+0.j, 0.+0.j, 0.+0.j,\n",
              "         0.+1.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n",
              "        [0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j,\n",
              "         0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j,\n",
              "         0.+0.j, 0.+1.j, 0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j, 1.+0.j, 0.+0.j,\n",
              "         0.+0.j, 0.+1.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n",
              "        [0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j,\n",
              "         0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j,\n",
              "         0.+0.j, 0.+0.j, 0.+1.j, 0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j, 1.+0.j,\n",
              "         0.+0.j, 0.+0.j, 0.+1.j, 0.+0.j, 0.+0.j, 0.+0.j],\n",
              "        [0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j,\n",
              "         0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j,\n",
              "         0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+1.j, 0.+0.j, 0.+0.j, 0.+0.j,\n",
              "         1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n",
              "        [0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j,\n",
              "         0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j,\n",
              "         0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+1.j, 0.+0.j, 0.+0.j,\n",
              "         1.+0.j, 1.+0.j, 0.+0.j, 0.+1.j, 0.+0.j, 0.+0.j],\n",
              "        [0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j,\n",
              "         0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j,\n",
              "         0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+1.j, 0.+0.j,\n",
              "         0.+0.j, 1.+0.j, 1.+0.j, 0.+0.j, 0.+1.j, 0.+0.j],\n",
              "        [0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j,\n",
              "         0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j,\n",
              "         0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j,\n",
              "         0.+1.j, 0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j],\n",
              "        [0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j,\n",
              "         0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j,\n",
              "         0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j,\n",
              "         0.+0.j, 0.+1.j, 0.+0.j, 1.+0.j, 1.+0.j, 0.+1.j],\n",
              "        [0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j,\n",
              "         0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j,\n",
              "         0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j,\n",
              "         0.+0.j, 0.+0.j, 0.+0.j, 0.+1.j, 0.+0.j, 1.+0.j]]),\n",
              " array([[(-1, 1), 0, (1, -3), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
              "         0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
              "        [(-1, 2), (-2, 2), (2, -3), 0, (2, -5), 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
              "         0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
              "        [0, 0, (-3, 3), 0, 0, (3, -6), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
              "         0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
              "        [0, (-2, 4), 0, (-4, 4), (4, -5), 0, 0, (4, -8), 0, 0, 0, 0, 0, 0,\n",
              "         0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
              "        [0, 0, (-3, 5), 0, (-5, 5), (5, -6), 0, 0, (5, -9), 0, 0, 0, 0, 0,\n",
              "         0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
              "        [0, 0, 0, 0, 0, (-6, 6), 0, 0, 0, (6, -10), 0, 0, 0, 0, 0, 0, 0,\n",
              "         0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
              "        [0, 0, 0, (-4, 7), 0, 0, (-7, 7), (7, -8), 0, 0, 0, (7, -12), 0,\n",
              "         0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
              "        [0, 0, 0, 0, (-5, 8), 0, 0, (-8, 8), (8, -9), 0, 0, 0, (8, -13),\n",
              "         0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
              "        [0, 0, 0, 0, 0, (-6, 9), 0, 0, (-9, 9), (9, -10), 0, 0, 0,\n",
              "         (9, -14), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
              "        [0, 0, 0, 0, 0, 0, 0, 0, 0, (-10, 10), 0, 0, 0, 0, (10, -15), 0,\n",
              "         0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
              "        [0, 0, 0, 0, 0, 0, (-7, 11), 0, 0, 0, (-11, 11), (11, -12), 0, 0,\n",
              "         0, (11, -16), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
              "        [0, 0, 0, 0, 0, 0, 0, (-8, 12), 0, 0, 0, (-12, 12), (12, -13), 0,\n",
              "         0, 0, (12, -17), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
              "        [0, 0, 0, 0, 0, 0, 0, 0, (-9, 13), 0, 0, 0, (-13, 13), (13, -14),\n",
              "         0, 0, 0, (13, -18), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
              "        [0, 0, 0, 0, 0, 0, 0, 0, 0, (-10, 14), 0, 0, 0, (-14, 14),\n",
              "         (14, -15), 0, 0, 0, (14, -19), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
              "        [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, (-15, 15), 0, 0, 0, 0,\n",
              "         (15, -20), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
              "        [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, (-11, 16), 0, 0, 0, 0, (16, -16),\n",
              "         0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
              "        [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, (-12, 17), 0, 0, 0, (-16, 17),\n",
              "         (17, -17), 0, 0, 0, (17, -21), 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
              "        [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, (-13, 18), 0, 0, 0,\n",
              "         (-17, 18), (18, -18), 0, 0, 0, (18, -22), 0, 0, 0, 0, 0, 0, 0, 0],\n",
              "        [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, (-14, 19), 0, 0, 0,\n",
              "         (-18, 19), (19, -19), 0, 0, 0, (19, -23), 0, 0, 0, 0, 0, 0, 0],\n",
              "        [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, (-15, 20), 0, 0, 0,\n",
              "         (-19, 20), (20, -20), 0, 0, 0, (20, -24), 0, 0, 0, 0, 0, 0],\n",
              "        [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, (-16, 21), 0, 0, 0,\n",
              "         0, (21, -21), 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
              "        [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, (-17, 22), 0, 0,\n",
              "         0, (-21, 22), (22, -22), 0, 0, (22, -25), 0, 0, 0, 0, 0],\n",
              "        [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, (-18, 23), 0,\n",
              "         0, 0, (-22, 23), (23, -23), 0, 0, (23, -26), 0, 0, 0, 0],\n",
              "        [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, (-19, 24),\n",
              "         0, 0, 0, (-23, 24), (24, -24), 0, 0, (24, -27), 0, 0, 0],\n",
              "        [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
              "         (-21, 25), 0, 0, 0, (25, -25), 0, 0, 0, 0, 0],\n",
              "        [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
              "         (-22, 26), 0, 0, (-25, 26), (26, -26), 0, (26, -28), 0, 0],\n",
              "        [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
              "         (-23, 27), 0, 0, (-26, 27), (27, -27), 0, (27, -29), 0],\n",
              "        [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
              "         0, 0, (-25, 28), 0, 0, (28, -28), 0, 0],\n",
              "        [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
              "         0, 0, 0, (-26, 29), 0, (-28, 29), (29, -29), (29, -30)],\n",
              "        [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
              "         0, 0, 0, 0, 0, (-28, 30), 0, (30, -30)]], dtype=object))"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Xdzb6KVH-UAH"
      },
      "source": [
        "!touch images/d.png\n",
        "!rm images/*.png"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gtxWzvMiUk3m"
      },
      "source": [
        "# Generate image sequence with distinct tilings\n",
        "\n",
        "The generated image are saved as *Files/images/frame_0001.png*."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "7vJSYMuHW_KU",
        "outputId": "4f4077d9-efe8-4243-c7ed-69a05ecd3226"
      },
      "source": [
        "# which frames to export\n",
        "# NB you can set the frame_index so that the export doesn't have to start with j=0,\n",
        "# or use a step value, e.g. range(100,640,10)\n",
        "frame_index = list(range(0,64, 1))\n",
        "\n",
        "for j,res in enumerate(getTilings(B), start=1):\n",
        "  \n",
        "  if j>max(frame_index):\n",
        "    break\n",
        "  elif j not in frame_index:\n",
        "    continue\n",
        "  \n",
        "  print(f'# {j}')\n",
        "  fig, ax = plt.subplots()\n",
        "\n",
        "  # matplotlib, colortable: https://stackoverflow.com/questions/22408237/named-colors-in-matplotlib/37232760\n",
        "  drawTiling(res, ax, vcolor='antiquewhite', hcolor='burlywood')\n",
        "\n",
        "  # export and show the result\n",
        "  plt.axis('off')\n",
        "  plt.savefig(\"images/frame_{:04d}.png\".format(j), dpi=None, transparent=True, bbox_inches='tight')\n",
        "  plt.show()\n",
        "\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "# 1\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAV0AAADnCAYAAAC9roUQAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAEu0lEQVR4nO3dwY0aWRhG0ceM1RQBWHYKzj+YScGtCYDCks0sZtssQOjW6+KcAFr/onVBb8F3uF6vA4DGX1sfAPBKRBcgJLoAIdEFCIkuQEh0AUKiCxASXYCQ6AKERBcgJLoAIdEFCIkuQEh0AUKiCxD6svUBvI7Tafm5rpdvW9/xkWU5vp/P6/et72D/Dn7EnMrhcLj++vefrc/40NvXH+N6vR62voP987wAEBJdgJDoAoREFyAkugAh0QUIiS5ASHQBQqILEBJdgJDoAoREFyAkugAh0QUIiS5ASHQBQqILEBJdgJC5Hm569qbZ8fg2Lpdfz/pzT/Xs22yucYvoctPMm2Zj/L9rNut9Nte4xfMCQEh0AUKiCxASXYCQ6AKERBcgJLoAIdEFCIkuQEh0AUKiCxASXYCQ6AKERBcgJLoAIdEFCIkuQEh0AULmenbklTbNxhhjOR7HerlsfcaHbK5xi+juiE2zx8182xg21/bE8wJASHQBQqILEBJdgJDoAoREFyAkugAh0QUIiS5ASHQBQqILEBJdgJDoAoREFyAkugAh0QUIiS5ASHQBQuZ6NvbMXTObZo+b+bYxbK7tiehubOZds8+wGzbrfTPfNobNtS15XgAIiS5ASHQBQqILEBJdgJDoAoREFyAkugAh0QUIiS5ASHQBQqILEBJdgJDoAoREFyAkugAh0QUIWY640zPndcaYe2Jn9gmbme+b+bYxnvt/Z/rnPqJ7J/M6j5v5vplvG2Pu+0z/3MfzAkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFC5nrudDotv9f1MuWH1ey7XDPfN/NtY8x937Ic/5zP699b3/FZiO6dbKQ9bub7Zr5tjLnvs5F2nym/sQHslegChEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChMz13Ol0Wn6u6+Xb1nd8ZOYdrTHmvm/m28aY+75lOb6fz+v3re/4LER3YzbXHjfzfTPfNoZdsy15XgAIiS5ASHQBQqILEBJdgJDoAoREFyAkugAh0QUIiS5ASHQBQqILEBJdgJDoAoREFyAkugAh0QUIiS5AyFzPxmyuPW7m+2a+bQy7ZlsS3R2ZeW9tjLl3w2a+bQybZnvieQEgJLoAIdEFCIkuQEh0AUKiCxASXYCQ6AKERBcgJLoAIdEFCIkuQEh0AUKiCxASXYCQ6AKERBcgZDliR2ae/hlj7gmbmW8bw7zOnoguN5n/eZx5HW7xvAAQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkLkebrK59jibZtwiumRm3lyzaUbF8wJASHQBQqILEBJdgJDoAoREFyAkugAh0QUIiS5ASHQBQqILEBJdgJDoAoREFyAkugAh0QUIiS5ASHQBQl+2PoDXsSzH97evP6bcXFuW4/vWN/AabKQBhDwvAIREFyAkugAh0QUIiS5ASHQBQqILEBJdgJDoAoREFyAkugAh0QUIiS5ASHQBQqILEPoPFxpo6XwlW9wAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 2\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 3\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 4\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 5\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 6\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 7\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 8\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 9\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 10\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 11\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 12\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 13\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAV0AAADnCAYAAAC9roUQAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAFDklEQVR4nO3dwW0bVxhG0UdD4IwKEOx1duokLaUCt5ROssvaQgoQRwjMLLwVgUgg7jxR5xQw+Ec2ro1Z6Ducz+cBQOPL3gcAfCaiCxASXYCQ6AKERBcgJLoAIdEFCIkuQEh0AUKiCxASXYCQ6AKERBcgJLoAIdEFCN3tfQCfx/39+uN02r7ufcdr1nV5en4+fdv7Dm7fwS8xp3I4HM4v//y19xmvOj48jvP5fNj7Dm6fzwsAIdEFCIkuQEh0AUKiCxASXYCQ6AKERBcgJLoAIdEFCIkuQEh0AUKiCxASXYCQ6AKERBcgJLoAIdEFCJnr4aJrb5oty3Fs28u1HndV177N5hqXiC4XzbxpNsavXbNZ77O5xiU+LwCERBcgJLoAIdEFCIkuQEh0AUKiCxASXYCQ6AKERBcgJLoAIdEFCIkuQEh0AUKiCxASXYCQ6AKERBcgZK7nhnymTbMxxliXZZy2be8zXmVzjUtE94bYNHu/mW8bw+baLfF5ASAkugAh0QUIiS5ASHQBQqILEBJdgJDoAoREFyAkugAh0QUIiS5ASHQBQqILEBJdgJDoAoREFyAkugAhcz07u+aumU2z95v5tjFsrt0S0d3ZzLtmH2E3bNb7Zr5tDJtre/J5ASAkugAh0QUIiS5ASHQBQqILEBJdgJDoAoREFyAkugAh0QUIiS5ASHQBQqILEBJdgJDoAoREFyBkOeKNrjmvM8bcEzuzT9jMfN/Mt41x3b93pn/eRnTfyLzO+x0fHsfff36/2vN++/2Pad/3s72r6Z//z+cFgJDoAoREFyAkugAh0QUIiS5ASHQBQqILEBJdgJDoAoREFyAkugAh0QUIiS5ASHQBQqILEBJdgJDoAoTu9j7go1nX5efx4XHKf6zWZRnHh8e9z8gsy3Ha912W41WfN/Of7bouP/e+4SMR3Tc6nbYvM29VzXrbGOPq0di2l2nf99rvetq2md91yv+EzMoPCyAkugAh0QUIiS5ASHQBQqILEBJdgJDoAoREFyAkugAh0QUIiS5ASHQBQqILEBJdgJDoAoREFyAkugChw/l83vuGD+X+fv1xOm1f977jNeuyjNO27X3GRcvxbmwv/077vGu69m3rchyn7eVqz7umdV2enp9P3/a+46MQ3Z0dDofzxNtX0+5yjTH3fTPfNsav+87n82HvOz4jnxcAQqILEBJdgJDoAoREFyAkugAh0QUIiS5ASHQBQqILEBJdgJDoAoREFyAkugAh0QUIiS5ASHQBQqILEDLXszOba+83830z3zaGXbM9ie4NmXlvbYy5d8Nmvm0Mm2a3xOcFgJDoAoREFyAkugAh0QUIiS5ASHQBQqILEBJdgJDoAoREFyAkugAh0QUIiS5ASHQBQqILEBJdgJDliBsy8/TPGHNP2Mx82xjmdW6J6HKR+Z/3M6/DJT4vAIREFyAkugAh0QUIiS5ASHQBQqILEBJdgJDoAoREFyAkugAh0QUIiS5ASHQBQqILEBJdgJDoAoREFyBkroeLbK69n00zLhFdMjNvrtk0o+LzAkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFCd3sfwOexrsvT8eFxys21dV2e9r6Bz8FGGkDI5wWAkOgChEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFC/wHv1FpImlAJhAAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 14\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 15\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 16\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 17\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 18\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAV0AAADnCAYAAAC9roUQAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAFAElEQVR4nO3dwW0bVxhG0UdD4IwKEOy1d+rELbmCtJROssvaQgoQKQdhFt6KgK0wd57IcwoY/ODi2ngLfbvT6TQAaHzY+gCAWyK6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFCogsQEl2A0N3WB3A77u/Xb4fD8ePWd7xmXZen5+fDp63v4Prt/BFzKrvd7vTy1x9bn/Gq/cPjOJ1Ou63v4Pp5XgAIiS5ASHQBQqILEBJdgJDoAoREFyAkugAh0QUIiS5ASHQBQqILEBJdgJDoAoREFyAkugAh0QUIiS5AyFwPZ11602xZ9uN4fLnU5y7q0rfZXOMc0eWsmTfNxvixazbrfTbXOMfzAkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFC5nquyC1tmo0xxros43A8bn3Gq2yucY7oXhGbZm83821j2Fy7Jp4XAEKiCxASXYCQ6AKERBcgJLoAIdEFCIkuQEh0AUKiCxASXYCQ6AKERBcgJLoAIdEFCIkuQEh0AUKiCxAy17OxS+6a2TR7u5lvG8Pm2jUR3Y3NvGv2HnbDZr1v5tvGsLm2Jc8LACHRBQiJLkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXICS6ACHLEb/okvM6Y8w9sTP7hM3M98182xiXvW/Z3z0djt9N//wk0f1F5nXebv/wOP78/beLfe/zl68X+97nL1/9dv/hW6Z/fp7nBYCQ6AKERBcgJLoAIdEFCIkuQEh0AUKiCxASXYCQ6AKERBcgJLoAIdEFCIkuQEh0AUKiCxASXYCQ6AKE7rY+4L1Z1+Wf/cPjlP9Yrcsy9g+PW5/xLvntqIjuLzocjh9m3dJ6Dxtpszocj347ElP+jw3gWokuQEh0AUKiCxASXYCQ6AKERBcgJLoAIdEFCIkuQEh0AUKiCxASXYCQ6AKERBcgJLoAIdEFCIkuQGh3Op22vuFdub9fvx0Ox49b3/GadVnG4Xjc+oyzlv3dOL78PeX31mU/DseXi3zr/zDzb7fs754Ox++fLvKxGyC6G9vtdqdZt7new+barPfNfNsYP+47nU67re+4RZ4XAEKiCxASXYCQ6AKERBcgJLoAIdEFCIkuQEh0AUKiCxASXYCQ6AKERBcgJLoAIdEFCIkuQEh0AUKiCxAy17Mxm2tvN/N9M982xhjrujw9Px/smm1AdK/IzHtrY8y9GzbzbWPYNLsmnhcAQqILEBJdgJDoAoREFyAkugAh0QUIiS5ASHQBQqILEBJdgJDoAoREFyAkugAh0QUIiS5ASHQBQpYjrsjM0z9jzD1hM/NtY5jXuSaiy1nmf97OvA7neF4ACIkuQEh0AUKiCxASXYCQ6AKERBcgJLoAIdEFCIkuQEh0AUKiCxASXYCQ6AKERBcgJLoAIdEFCIkuQMhcD2fZXHs7m2acI7pkZt5cs2lGxfMCQEh0AUKiCxASXYCQ6AKERBcgJLoAIdEFCIkuQEh0AUKiCxASXYCQ6AKERBcgJLoAIdEFCIkuQEh0AUJ3Wx/A7VjX5Wn/8Djl5tq6Lk9b38BtsJEGEPK8ABASXYCQ6AKERBcgJLoAIdEFCIkuQEh0AUKiCxASXYCQ6AKERBcgJLoAIdEFCIkuQOhfCmxY2ZVL7/EAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 19\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 20\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 21\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 22\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 23\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 24\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 25\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAV0AAADnCAYAAAC9roUQAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAFMUlEQVR4nO3dwW0bVxhG0UdD4VAFCPbaO3eSllxBWkon2WVtIQWItIMwCyE7EYiE8Z0n8pwCBv9Y8LUwC3+78/k8AGh82PoAgFsiugAh0QUIiS5ASHQBQqILEBJdgJDoAoREFyAkugAh0QUIiS5ASHQBQqILEBJdgNDd1gdwO+7vD9+Ox9PHre94yeGwPD49HT9tfQfXb+c/Maey2+3O3//6Y+szXrR/+DLO5/Nu6zu4fj4vAIREFyAkugAh0QUIiS5ASHQBQqILEBJdgJDoAoREFyAkugAh0QUIiS5ASHQBQqILEBJdgJDoAoREFyBkroeL1t40W5b9OJ2+r/W4Va19m801LhFdLpp502yM512zWe+zucYlPi8AhEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXIGSu54rc0qbZGGMclmUcT6etz3iRzTUuEd0rYtPs7Wa+bQyba9fE5wWAkOgChEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChMz1bGzNXTObZm83821jrH/fsr97PJ5+2FzbgOhubOZds/ewG/bn77+t8qzPv369mXcd4/l9ba5tw+cFgJDoAoREFyAkugAh0QUIiS5ASHQBQqILEBJdgJDoAoREFyAkugAh0QUIiS5ASHQBQqILEBJdgNDd1ge8N2vO64zxPLGzf/iy1uNWdViWaW9b28w/hzGe71vbbrdbZTbG9M/riO4rHY+nj7POuvyMSZdZ33WMsWokT6fvN/Ou/1lx6mi1X0Jugc8LACHRBQiJLkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiZ63mlw2H5Z//w5Sb+sZp+N2x/Nz7/+nW1Z93Ku44xxv4Xf/W34k/+lY7H04dZt7TWjsZ72A2b9b6Zbxvj52yu8f/cxG9sALMQXYCQ6AKERBcgJLoAIdEFCIkuQEh0AUKiCxASXYCQ6AKERBcgJLoAIdEFCIkuQEh0AUKiCxASXYDQ7nw+b33Du3J/f/h2PJ4+bn3HS5b93Th9/3va563tsCzjeDptfcaLZr5tjHV/tsv+7vF4+vFplYfdANHd2G63O8+6pfUedr5mvW/m28Z4vu98Pu+2vuMW+bwAEBJdgJDoAoREFyAkugAh0QUIiS5ASHQBQqILEBJdgJDoAoREFyAkugAh0QUIiS5ASHQBQqILEBJdgJC5no3NvLk2+87XzPfNfNsYYxwOy+PT09Gu2QZE94rMvLc2xty7YTPfNoZNs2vi8wJASHQBQqILEBJdgJDoAoREFyAkugAh0QUIiS5ASHQBQqILEBJdgJDoAoREFyAkugAh0QUIiS5AyHLEFZl5+meMuSdsZr5tDPM610R0ucj8z9uZ1+ESnxcAQqILEBJdgJDoAoREFyAkugAh0QUIiS5ASHQBQqILEBJdgJDoAoREFyAkugAh0QUIiS5ASHQBQqILEDLXw0U2197OphmXiC6ZmTfXbJpR8XkBICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXICS6AKG7rQ/gdhwOy+P+4cuUm2uHw/K49Q3cBhtpACGfFwBCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQj9C5KmRvq0bI/xAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 26\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 27\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 28\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 29\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 30\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 31\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAV0AAADnCAYAAAC9roUQAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAFNklEQVR4nO3dwW0bVxhG0ceA5lAFCPY6O3eSllJBWkon2WVtIQWIlI0wC29FwDImd57IcwoY/JSgK2EW+naXy2UA0Phl6wMA7onoAoREFyAkugAh0QUIiS5ASHQBQqILEBJdgJDoAoREFyAkugAh0QUIiS5ASHQBQvutD+B+PDwcv5xO549b3/Ga43F5en4+fdr6Dm7fzj8xp7Lb7S4v//y19RmvOjx+HpfLZbf1Hdw+rxcAQqILEBJdgJDoAoREFyAkugAh0QUIiS5ASHQBQqILEBJdgJDoAoREFyAkugAh0QUIiS5ASHQBQqILEDLXw1Vrb5oty2Gczy9rPW5Va99mc41rRJerZt40G+P7rtms99lc4xqvFwBCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFCogsQMtdzQ+5p02yMMY7LMk7n89ZnvGrt25bD/ul0/mpz7QaI7g15D5tmf//5x2rP+/W336feSFv7s9pcuw1eLwCERBcgJLoAIdEFCIkuQEh0AUKiCxASXYCQ6AKERBcgJLoAIdEFCIkuQEh0AUKiCxASXYCQ6AKERBcgtN/6gHu35q7ZshzG4fHzGo96F2b+vMtyWP2Zu91utW0tm2vbEd2NnU7nj/e087Wm8/ll6o20ta38vVhtwJS38XoBICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXIGQ54o3WnNcZY+7JmbUdPuxXXY9YDvtpv3bLYd3Peviw/o/qWvM/pn/eRnTfyLzOz3v5+m3qeZ1Zbxtj7vkf0z9v4/UCQEh0AUKiCxASXYCQ6AKERBcgJLoAIdEFCIkuQEh0AUKiCxASXYCQ6AKERBcgJLoAIdEFCIkuQEh0AULmet7oeFz+PTx+votfVve0aXZclmlvG+N9bK7xY3zl3+h0Ov8y65bW2tGYedNsjLl3zWa+bYz/Z3ONH3MXf7EBzEJ0AUKiCxASXYCQ6AKERBcgJLoAIdEFCIkuQEh0AUKiCxASXYCQ6AKERBcgJLoAIdEFCIkuQEh0AUK7y+Wy9Q3vysPD8cvpdP649R2vWQ77cX75Nu3z1nZclnE6n7c+41Uz3zbGut/b5bB/Op2/flrlYXdAdDe22+0us25pvYedr1nvm/m2Mb7fd7lcdlvfcY+8XgAIiS5ASHQBQqILEBJdgJDoAoREFyAkugAh0QUIiS5ASHQBQqILEBJdgJDoAoREFyAkugAh0QUIiS5AyFzPxmbeXJt952vm+2a+bYwxjsfl6fn5ZNdsA6J7Q2beWxtj7t2wmW8bw6bZLfF6ASAkugAh0QUIiS5ASHQBQqILEBJdgJDoAoREFyAkugAh0QUIiS5ASHQBQqILEBJdgJDoAoREFyBkOeKGzDz9M8bcEzYz3zaGeZ1bIrpcZf7n55nX4RqvFwBCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFCogsQMtfDVTbXfp5NM64RXTIzb67ZNKPi9QJASHQBQqILEBJdgJDoAoREFyAkugAh0QUIiS5ASHQBQqILEBJdgJDoAoREFyAkugAh0QUIiS5ASHQBQvutD+B+HI/L0+Hx85Sba8fj8rT1DdwHG2kAIa8XAEKiCxASXYCQ6AKERBcgJLoAIdEFCIkuQEh0AUKiCxASXYCQ6AKERBcgJLoAIdEFCP0H+xA6XQkz1hIAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 32\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 33\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 34\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 35\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 36\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 37\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 38\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 39\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 40\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 41\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 42\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 43\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 44\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAV0AAADnCAYAAAC9roUQAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAFK0lEQVR4nO3dMW5bRxhG0aGhiNQCBLt2Fe3ETRbkIlWKLChNdpJUqS1kASIlB0yhVgQs4fm+MXnOAga/AONaeIW+zfF4HAA03q19AMAlEV2AkOgChEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiJLkDoau0DuBw3N7sv+/3h/dp3vGS3294/POw/rH0H52/jj5hT2Ww2x8d//1r7jBdd396N4/G4WfsOzp/PCwAh0QUIiS5ASHQBQqILEBJdgJDoAoREFyAkugAh0QUIiS5ASHQBQqILEBJdgJDoAoREFyAkugAh0QUImevhpKU3zbbb63E4PC713KKWvs3mGqeILifNvGk2xvOu2az32VzjFJ8XAEKiCxASXYCQ6AKERBcgJLoAIdEFCIkuQEh0AUKiCxASXYCQ6AKERBcgJLoAIdEFCIkuQEh0AUKiCxAy13NGLmnTbIwxdtvt2B8Oa5/xIptrnCK6Z8Sm2dvNfNsYNtfOic8LACHRBQiJLkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiZ61nZkrtmNs3ebubbxlj+vu311f3+8GRzbQWiu7KZd82ub+/GP3/+vth7Hz99nva9mW/7Xu/ZXFuHzwsAIdEFCIkuQEh0AUKiCxASXYCQ6AKERBcgJLoAIdEFCIkuQEh0AUKiCxASXYCQ6AKERBcgJLoAoau1D/jRLDmvM8bzxM717d1Sz8E322w2i8zGmP55HdF9pf3+8P6S5nU4XwtOHS32S8gl8HkBICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXICS6AKHN8bjITNLFuLnZ/bffH6b9z2rJuZ6ff/l1PD59Xey97fXVODzO+d7Mt32P965/uhp///HbIm99/PR5HI/HzSKPXQAbaa+03x/ezbyRtqTHp69j1p91jOefd9b7Zr5tjOX/rfDtpv2NDeAciS5ASHQBQqILEBJdgJDoAoREFyAkugAh0QUIiS5ASHQBQqILEBJdgJDoAoREFyAkugAh0QUIiS5AyEbaK93c7L7s94f3a9/xktl3uZa2227H/nBY+4wXzXzbGIvvy93vD08fFnnsAojuyjabzXHWLa0fYedr1vtmvm2M5/uMSa7D5wWAkOgChEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChMz1rGzmzbXZd75mvm/m28YYY7fb3j887O2arUB0z8jMe2tjzL0bNvNtY9g0Oyc+LwCERBcgJLoAIdEFCIkuQEh0AUKiCxASXYCQ6AKERBcgJLoAIdEFCIkuQEh0AUKiCxASXYCQ6AKELEeckZmnf8aYe8Jm5tvGMK9zTkSXk8z/vJ15HU7xeQEgJLoAIdEFCIkuQEh0AUKiCxASXYCQ6AKERBcgJLoAIdEFCIkuQEh0AUKiCxASXYCQ6AKERBcgJLoAIXM9nGRz7e1smnGK6JKZeXPNphkVnxcAQqILEBJdgJDoAoREFyAkugAh0QUIiS5ASHQBQqILEBJdgJDoAoREFyAkugAh0QUIiS5ASHQBQqILELpa+wAux263vb++vZtyc223296vfQOXwUYaQMjnBYCQ6AKERBcgJLoAIdEFCIkuQEh0AUKiCxASXYCQ6AKERBcgJLoAIdEFCIkuQEh0AUL/A8QQYUh4J1ENAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 45\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 46\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 47\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 48\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 49\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAV0AAADnCAYAAAC9roUQAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAFMUlEQVR4nO3dwW0bVxhG0UdD4YwKEOx1duokLaWCtJROssvaRgowqRhhFtqKCxvjO0/kOQUMflHClTALfYfL5TIAaHzY+wCAeyK6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFCogsQEl2A0MPeB3A/Hh/Xz6fT+ePed7xlXZcvX7+ePu19B7fv4J+YUzkcDpeXf/7a+4w3HZ+ex+VyOex9B7fP6wWAkOgChEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChMz1cNXWm2bLchzn88tWj9vU1rfZXOMa0eWqmTfNxnjdNZv1PptrXOP1AkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFC5npuyD1tmo0xxros43Q+733Gm2yucY3o3hCbZj9u5tvGsLl2S7xeAAiJLkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiJLkDIXM/Ottw1s2n242a+bQyba7dEdHc2867Z8el5/P3nH5s979ffft/8eTN/drPeNobNtT15vQAQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFCogsQetj7gPdmy3mdMV5nWI5Pz1s97q6syzLtZzfzbWO8/twdDodNZmNM/3wf0f1Op9P546wzLD9jXmdmp/N52kmcn/G9mPhr3eyPkHvg9QJASHQBQqILEBJdgJDoAoREFyAkugAh0QUIiS5ASHQBQqILEBJdgJDoAoREFyAkugAh0QUIiS5ASHQBQuZ6vtO6Lv8dn57v4pfV8ZeHTSd7luO2z1sn3pdbluOmz5t5c21dl//2vuE9Ed3vdDqdP0y8VbXp817+/TbtLtcYr1/vrPdt/b2YfA/uLv4I2YoPCyAkugAh0QUIiS5ASHQBQqILEBJdgJDoAoREFyAkugAh0QUIiS5ASHQBQqILEBJdgJDoAoREFyAkugChw+Vy2fuGd+Xxcf18Op0/7n3HW5bjwzi/fJv2eVtbl2Wczue9z3jT1p/duhzH6fyy2fO2tK7Ll69fT5/2vuO9EN2dHQ6Hy8TbV9Puco0x930z3zbG632Xy+Ww9x33yOsFgJDoAoREFyAkugAh0QUIiS5ASHQBQqILEBJdgJDoAoREFyAkugAh0QUIiS5ASHQBQqILEBJdgJDoAoTM9exs5s21mTfIxpj7vplvG8Ou2Z5E94bMvLc2xty7YTPfNoZNs1vi9QJASHQBQqILEBJdgJDoAoREFyAkugAh0QUIiS5ASHQBQqILEBJdgJDoAoREFyAkugAh0QUIiS5AyHLEDZl5+meMuSdsZr5tDPM6t0R0ucr8z48zr8M1Xi8AhEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXIGSuh6tsrv04m2ZcI7pkZt5cs2lGxesFgJDoAoREFyAkugAh0QUIiS5ASHQBQqILEBJdgJDoAoREFyAkugAh0QUIiS5ASHQBQqILEBJdgJDoAoQe9j6A+7Guy5fj0/OUm2vrunzZ+wbug400gJDXCwAh0QUIiS5ASHQBQqILEBJdgJDoAoREFyAkugAh0QUIiS5ASHQBQqILEBJdgJDoAoT+B4/YSwn95JsyAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 50\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAV0AAADnCAYAAAC9roUQAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAFLElEQVR4nO3dwW0bVxhG0UdD5owLEOx1duokLaWCtJROssvaRgowqRhmFtqKCwvjO8/kOQUMfonQlTALfYfL5TIAaLzb+wCAeyK6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFCogsQEl2A0MPeB3A/PnxYP59O54973/GadV2+fP16+rT3Hdy+g39iTuVwOFye//177zNedXx8GpfL5bD3Hdw+rxcAQqILEBJdgJDoAoREFyAkugAh0QUIiS5ASHQBQqILEBJdgJDoAoREFyAkugAh0QUIiS5ASHQBQqILEDLXw1Vbb5oty3Gcz89bPW5TW99mc41rRJerZt40G+Nl12zW+2yucY3XCwAh0QUIiS5ASHQBQqILEBJdgJDoAoREFyAkugAh0QUIiS5ASHQBQqILEBJdgJDoAoREFyAkugAh0QUImeu5Ife0aTbGGOuyjNP5vPcZr7K5xjWie0Nsmr3dzLeNYXPtlni9ABASXYCQ6AKERBcgJLoAIdEFCIkuQEh0AUKiCxASXYCQ6AKERBcgJLoAIdEFCIkuQEh0AUKiCxASXYCQuZ6dbblrZtPs7Wa+bQyba7dEdHc2867Z8fFp/PPXn5s977ff/5j2eT/jtlk/1zFsru3J6wWAkOgChEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFCogsQEl2A0MPeB/xqtpzXGeNlhuX4+LTV45jE7J/rshzH4XDYZDbG9M+PEd0fdDqdP846w/Iz5nV4m/P5+W7mf46PT5v9EXIPvF4ACIkuQEh0AUKiCxASXYCQ6AKERBcgJLoAIdEFCIkuQEh0AUKiCxASXYCQ6AKERBcgJLoAIdEFCIkuQMhczw9a1+X78fHpLn5ZHd8/bDrZsxznfd7Wtx3fb/ujtS7LtJtr67p83/uGX4no/qDT6fxu4q2qTZ/3/N+3aXe5xnj5eme9b+vP4nQ+z/y13sUfIVvxzQIIiS5ASHQBQqILEBJdgJDoAoREFyAkugAh0QUIiS5ASHQBQqILEBJdgJDoAoREFyAkugAh0QUIiS5A6HC5XPa+4Zfy4cP6+XQ6f9z7jtcsx4dxfv427fO2ti7LOJ3Pe5/xqq2/d+tyHKfz82bP29K6Ll++fj192vuOX4Xo7uxwOFwm3r6adpdrjLnvm/m2MV7uu1wuh73vuEdeLwCERBcgJLoAIdEFCIkuQEh0AUKiCxASXYCQ6AKERBcgJLoAIdEFCIkuQEh0AUKiCxASXYCQ6AKERBcgZK5nZzNvrs28QTbG3PfNfNsYds32JLo3ZOa9tTHm3g2b+bYxbJrdEq8XAEKiCxASXYCQ6AKERBcgJLoAIdEFCIkuQEh0AUKiCxASXYCQ6AKERBcgJLoAIdEFCIkuQEh0AUKWI27IzNM/Y8w9YTPzbWOY17klostV5n/ezrwO13i9ABASXYCQ6AKERBcgJLoAIdEFCIkuQEh0AUKiCxASXYCQ6AKERBcgJLoAIdEFCIkuQEh0AUKiCxASXYCQuR6usrn2djbNuEZ0ycy8uWbTjIrXCwAh0QUIiS5ASHQBQqILEBJdgJDoAoREFyAkugAh0QUIiS5ASHQBQqILEBJdgJDoAoREFyAkugAh0QUIPex9APdjXZcvx8enKTfX1nX5svcN3AcbaQAhrxcAQqILEBJdgJDoAoREFyAkugAh0QUIiS5ASHQBQqILEBJdgJDoAoREFyAkugAh0QUI/Q+6OEw5ADSKRgAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 51\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 52\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAV0AAADnCAYAAAC9roUQAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAFK0lEQVR4nO3dwW0bVxhG0cdA4dAFCPbaO3fillxBWkon2WVtIQWYIwdhFkJ2IhAbgztP5DkFDH6I0pUwC32Hy+UyAGj8svcBAPdEdAFCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXICS6AKGHvQ/gfrx7d/p6Pq/v977jNafT8vTt2/nD3ndw+w7+iTmVw+Fwef7rj73PeNXx8dO4XC6Hve/g9nm9ABASXYCQ6AKERBcgJLoAIdEFCIkuQEh0AUKiCxASXYCQ6AKERBcgJLoAIdEFCIkuQEh0AUKiCxASXYCQuR6u2nrTbFmOY12ft3rcpra+zeYa14guV828aTbGy67ZrPfZXOMarxcAQqILEBJdgJDoAoREFyAkugAh0QUIiS5ASHQBQqILEBJdgJDoAoREFyAkugAh0QUIiS5ASHQBQqILEDLXc0PuadNsjDFOyzLO67r3Ga+yucY1ontDbJr9vJlvG8Pm2i3xegEgJLoAIdEFCIkuQEh0AUKiCxASXYCQ6AKERBcgJLoAIdEFCIkuQEh0AUKiCxASXYCQ6AKERBcgJLoAIXM9O9ty18ym2c+b+bYxbK7dEtHd2cy7Zm9hN+zP33/b5FkfP3/Z7Fn/PW/2r53NtX14vQAQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFCogsQetj7gLdmy3mdMV5mWI6Pn7Z63KZOyzLtbbOb+XMd4+WzPRwOm8zGLMeHp/P63fTP/yS6P+h8Xt/POsOy5XzNGG9jcmZW6/q8+Wcx6/M+fv6y2R8h98DrBYCQ6AKERBcgJLoAIdEFCIkuQEh0AUKiCxASXYCQ6AKERBcgJLoAIdEFCIkuQEh0AUKiCxASXYCQ6AKEzPX8oNNp+ef4+OkuflnNvvO1HB/Gx89fpnvWGGMcf/Wjxet8Z/yg83n9ZdbdsK0Dua7P02+kzXrfzL+s2Ndd/MUGMAvRBQiJLkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQgdLpfL3je8Ke/enb6ez+v7ve94zXJ8GOvz39M+b2unZRnndd37jFfN/lls+bzl+PB0Xr9/2ORhd0B0d3Y4HC4z73zNetsYc983821jvNx3uVwOe99xj7xeAAiJLkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiJLkDIXM/OZt5cm3mDbIy575v5tjHGOJ2Wp2/fznbNdiC6N2TmvbUx5t4Nm/m2MWya3RKvFwBCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFCliNuyMzTP2PMPWEz821jmNe5JaLLVeZ/fp55Ha7xegEgJLoAIdEFCIkuQEh0AUKiCxASXYCQ6AKERBcgJLoAIdEFCIkuQEh0AUKiCxASXYCQ6AKERBcgJLoAIXM9XGVz7efZNOMa0SUz8+aaTTMqXi8AhEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXIPSw9wHcj9NpeTo+fppyc+10Wp72voH7YCMNIOT1AkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXICS6AKF/AQOUSac+1xsLAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 53\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 54\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 55\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 56\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAV0AAADnCAYAAAC9roUQAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAFIklEQVR4nO3dwW0bVxhG0UdD5lAFCPbaO3XillxBWkon2WVtIQWYlI0wC21FIBbGd57JcwoY/AKlK2EW+nbn83kA0Hi39QEAt0R0AUKiCxASXYCQ6AKERBcgJLoAIdEFCIkuQEh0AUKiCxASXYCQ6AKERBcgJLoAobutD+B23N8fvh6Ppw9b3/Gaw2F5+vbt+HHrO7h+O//EnMputzs///PX1me8av/wOM7n827rO7h+Xi8AhEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXIGSuh4vW3jRblv04nZ7Xetyq1r7N5hqXiC4XzbxpNsbLrtms99lc4xKvFwBCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFCogsQMtdzRW5p02yMMQ7LMo6n09ZnvMrmGpeI7hWxafZ2M982hs21a+L1AkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFC5no2tuaumU2zt5v5tjFsrl0T0d3YzLtm+4fH8feff6z2vE+fv0z7vF9x26yf6xg217bk9QJASHQBQqILEBJdgJDoAoREFyAkugAh0QUIiS5ASHQBQqILEBJdgJDoAoREFyAkugAh0QUIiS5A6G7rA343a87rjPEyw7J/eFzrcUxi9s/1sCxjt9utMhuz7O+ejqfvpn/+J9H9Scfj6cOsMyy/Yl6HtzmdnqedJlr7eZ8+f1ntj5Bb4PUCQEh0AUKiCxASXYCQ6AKERBcgJLoAIdEFCIkuQEh0AUKiCxASXYCQ6AKERBcgJLoAIdEFCIkuQEh0AULmen7S4bD8u394vIlfVvv3d6tO9iz7eZ+39m379360eJ3vjJ90PJ7ezbyRtqbn7z/GrF/rGC9f76z3zTxKybZu4i82gFmILkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiJLkBodz6ft77ht3J/f/h6PJ4+bH3Ha5b93Tg9/5j2eWs7LMs4nk5bn/Gq2T+LNZ+37O+ejqfvH1d52A0Q3Y3tdrvzzDtfs942xtz3zXzbGC/3nc/n3dZ33CKvFwBCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFCogsQMtezsZk312beIBtj7vtmvm2MMQ6H5enbt6Ndsw2I7hWZeW9tjLl3w2a+bQybZtfE6wWAkOgChEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkOWIKzLz9M8Yc0/YzHzbGOZ1ronocpH5n7czr8MlXi8AhEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXIGSuh4tsrr2dTTMuEV0yM2+u2TSj4vUCQEh0AUKiCxASXYCQ6AKERBcgJLoAIdEFCIkuQEh0AUKiCxASXYCQ6AKERBcgJLoAIdEFCIkuQEh0AUJ3Wx/A7Tgclqf9w+OUm2uHw/K09Q3cBhtpACGvFwBCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQj9B71hSuBQbY13AAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 57\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 58\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 59\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 60\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 61\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 62\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "# 63\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAV0AAADnCAYAAAC9roUQAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAFLElEQVR4nO3dwW0bVxhG0UdDJqkCBHvtnTpxS64gLaWT7LK2kALMkY0wC21FIFYmd57JcwoY/Caoa2EW+nbn83kA0Hi39QEAt0R0AUKiCxASXYCQ6AKERBcgJLoAIdEFCIkuQEh0AUKiCxASXYCQ6AKERBcgJLoAobutD+B23N8fv55Oy4et73jN8Xh4+vbt9HHrO7h+O3/EnMputzs///XH1me8av/wOM7n827rO7h+Xi8AhEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXIGSuh4vW3jQ7HPZjWZ7Xetyq1r7N5hqXiC4XzbxpNsbLrtms99lc4xKvFwBCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFCogsQMtdzRW5p02yMMY6Hwzgty9ZnvMrmGpeI7hWxafZ2M982hs21a+L1AkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFC5no2tuaumU2zt5v5tjFsrl0T0d3YzLtm+4fH8efvv632vE+fv6z+vJk/u1lvG8Pm2pa8XgAIiS5ASHQBQqILEBJdgJDoAoREFyAkugAh0QUIiS5ASHQBQqILEBJdgJDoAoREFyAkugAh0QUI3W19wK9mzXmdMV5mWPYPj2s97qbM/NkdD4dpbxvj5b7dbrfKbMxhf/d0Wr6b/vmXRPcnnU7Lh1lnWP6PeZ2ZLcvzav/eW5oSGmPd78qnz19W+yXkFni9ABASXYCQ6AKERBcgJLoAIdEFCIkuQEh0AUKiCxASXYCQ6AKERBcgJLoAIdEFCIkuQEh0AUKiCxASXYCQuZ6fdDwe/t4/PN7Ef1b793erTvYc9us+b/9+3q/vzPttY7zcxzbm/dZO6nRa3s26fbX2D/nz9x/T73zNalmefXa86iZ+YwOYhegChEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChHbn83nrG34p9/fHr6fT8mHrO15z2N+N5fnHtM9b25r3+ez+07OeTsv3j6s87AaI7sZ2u9151i2t/cPj9Dtfs943821jvNx3Pp93W99xi7xeAAiJLkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiJLkDIXM/GZt5cOx4O47QsW59x0cz3zXzbGGMcj4enb99Ods02ILpXZOa9tTHm3g2b+bYxbJpdE68XAEKiCxASXYCQ6AKERBcgJLoAIdEFCIkuQEh0AUKiCxASXYCQ6AKERBcgJLoAIdEFCIkuQEh0AUKWI67IzNM/Y8w9YTPzbWOY17kmostF5n/ezrwOl3i9ABASXYCQ6AKERBcgJLoAIdEFCIkuQEh0AUKiCxASXYCQ6AKERBcgJLoAIdEFCIkuQEh0AUKiCxASXYCQuR4usrn2djbNuER0ycy8uWbTjIrXCwAh0QUIiS5ASHQBQqILEBJdgJDoAoREFyAkugAh0QUIiS5ASHQBQqILEBJdgJDoAoREFyAkugAh0QUI3W19ALfjeDw87R8ep9xcOx4PT1vfwG2wkQYQ8noBICS6ACHRBQiJLkBIdAFCogsQEl2AkOgChEQXICS6ACHRBQiJLkBIdAFCogsQEl2A0D/y+0yqLLt0PwAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6iydlmH3VMR9"
      },
      "source": [
        "## Convert image sequence into a gif animation at *Files/tiling.gif*"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qegkX1K0hk5n"
      },
      "source": [
        "!convert -delay 25 -loop 0 images/*.png -rotate -90 -trim +repage tiling.gif"
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}