Hexagonal Game of Life

This repository contains code for a hexagonal game of life being run on a teensy 4.0 with the teensy audio adaptor.

It runs continuous game of life simulations; however, when the algorithm detects that the game is over, it will play an ending.wav audio track which is stored on an SD card in the audio adaptor board.

Dependencies

This project uses PJRC's Teensyduino IDE which already include some of the libraries required to get this project running.

We also need Adafruit's Adafruit_NeoPixel library. I suggest following the link's installation instructions.

Debugging

The serial_view allows us to see the game of life on a serial terminal window.

Hardware

The hardware in this project includes:

• WS2812 LED strips
• Teensy 4.0
• PJRC's Audio Adaptor shield
• 5V (3A) power supply
• A 5V Speaker with Audio jack input
• Enclosure
  • Hexagonal shelf
  • 3D printed parts
  • White plastic for diffusing the LEDs

Algorithms

Game of life

Each cell has between 3 to 6 neighbours (the 6 corners having 3, edges having 4 and others having 6).

On each iteration, we follow these rules:

• Life begins or continues on cells with 2 or 3 living neighbours
• Living cells with 1 or 0 living neighbours die of loneliness
• Living cells with 4 or more living neighbours die of overpopulation

These rules are similar to the square-grid game of life, but the numbers differ to work better for a hexagonal grid.

It is possible that the game of life gets stuck in a loop. This often happens once a pattern develops some symmetry.

End of Life

An End of Life (EoL) algorithm was designed to detect when the game gets stuck in a loop. Once end of life is detected, the ending.wav file plays, and the game restarts near the end of the track.

The EoL algorithm is:

• On each step, calculate a uint64_t entry value which represents the current board.
  • There are 61 cells, each represented by 61 bits in the entry value.
• We have an eolEntries array, which stores 16 values:
  • Value 0 is stored on each game step
  • Value 1 is stored on every 2nd game step
  • Value 2 is stored on every 4th game step
  • Values 3 to 16 is stored on every 2^nth game step
• On each step, we check if the current entry matches any of the previous values in eolEntries
• If it does, the End of Life sequence begins

This algorithm allows us to detect loops as long as 65536 steps long using only 128 bytes of RAM.