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Conway's Game of Life is generalized to a continuous domain. OpenGL and GLSL shaders are used for real-time 2D and 3D graphics. Time stepping is done via a real to complex FFT based convolution operation. There are also two deliberately simple test implementations in FreeBasic and Matlab. A 2D version on a sphere shows that it is really not dependent on the underlying grid.
Explore procedural worlds on your GPU. Worlds are defined by GLSL programs that map XYZ coordinates to the distance to the nearest surface. Design your own worlds, modify parameters in realtime and render hires videos of your recorded journey.