The Axioma plugin was developed for the open-source VCV Rack library, using existing C++ templates provided in the VCV Manual. The current list of Axioma modules is the following:
A few patch examples (with VCV fundamental modules) can be found in the examples folder.
This module can be used as a sequencer to generate CV, GATE and TRIGGER outputs according to the mapped positions on the bifurcation map. The positions are obtained based on iterations of a selected function type f(n). The available function options are:
Each function can also iterate itself a number of times f(f(...)). The module contains a COBWEB DIAGRAM providing a visualization of the function shape and the last iteration points. The bifurcation parameter r(t) can be varied dynamically changing the behavior of each function and creating a specific distribution on the BIFURCATION MAP over time. The module contains both an input for external clock EXT and internal clock INT with input CV control. The iterated function is computed at each clock time. There are 4 options to set a mapping configuration of number of sections: 1, 2, 4 and 8. The CV, GATE and TRIG outputs are generated when the position reaches the corresponding map section where the port is located. The output CV level range will be from minimum (0V) to maximum (10V) within each map section.
The Tesseract module provides output CV control (0 - 10V) based on the position of each vertex of a rotating Tesseract projected on a 2D space (X,Y). The rotation speed of each plane in the 4D space (XY,YZ,XZ,XW,YW and ZW) can be controlled by input CV and/or the available Knobs. The perspective DISTANCE can also be set (CV and Knob) and provides a change in the voltage dynamic range of the output CVs
The Ikeda module is based on the dynamic system map proposed by Kensuke Ikeda which describes a chaotic behavior within a specific parameter range. The 2D example of the model used in this module can be described by the following equations:
The main parameter is the u value, which can be altered in the module and it is restricted to the 0.6 - 0.9 range (clamped). An additional parameter t was added to set a different weight ( 0.25 - 3.5 ) in the tn computation, which leads to a reshape of the chaotic maps. Output CVs are generated based on the (X,Y) positions obtained with this model. Each output CV level can be weighted by the available LEVEL knobs.
The Rhodonea module is a VCO with two oscillators defined by XY coordinates of Rhodonea curves. It follows the idea of polygonal synthesis where the wave shapes are created based on a projection of polar into cartesian coordinates. In this module, the Rhodonea curves (or Roses) are drawn on the XY plane using the following equations:
One can observe that the radial coordinate is defined by a cosine function with a frequency weight based on a ratio between parameters n and d. An additional parameter a can be used as a wet/dry control between a pure sine (with a specific pitch) and the harmonics generated by the curves. By varying the angle parameter, the curves are rotated which corresponds to phase variation in the waves. All parameters can be set both using input CV and/or the available Knobs. The outputs correspond to the axis color: X - cyan, Y - pink.
In case of any problem please add an issue to the tracker of this repository. Please also feel free to contact me at kaue.werner@gmail.com.