Conway's Game of Life for Curved Surfaces
Conway's Game of Life, a classic cellular automaton, inspires SmoothLife by Stephan Rafler. SmoothLife adapts Life's rules to continuous spaces using differential equations and sigmoid functions, providing a novel perspective on cellular automata.
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Conway's Game of Life is a well-known cellular automaton with simple rules that create complex patterns. It has been a popular project for novice programmers since its invention in 1970 by John Conway. The game's rules involve cells transitioning between alive and dead states based on the number of neighbors they have. Recently, a generalization of the Game of Life to smooth spaces, called SmoothLife, was proposed by Stephan Rafler. In SmoothLife, the traditional grid of cells is replaced by an effective grid obtained through averaging over a disk. Transition functions are defined by differential equations derived from a smooth interpolation of the original Game of Life rules. The concept involves representing cell states and neighborhood counts with continuous values and using sigmoid functions for state transitions. The implementation of SmoothLife requires discretizing the field and solving for coefficients to approximate the solution. Rafler's work introduces a new perspective on extending Conway's Game of Life to continuous domains, offering a fresh approach to cellular automata simulations.
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11 comments> If you want to try out SmoothLife yourself in your browser, I made a few jsFiddles which illustrate the basic principle. Here is a Fourier based implementation that follows the discussion in this article pretty closely: http://jsfiddle.net/mikola/aj2vq/
> I also made a second WebGL/GPU based implementation that uses a discretization similar to that proposed in Rafler’s original paper: http://jsfiddle.net/mikola/2jenR/
The jsfiddles seem to still be alive, but the "Run" button doesn't work for me. Anyone have any luck with them?
webgl implementation of SmoothLife from the comments section of the YouTube video linked in this article
Conway’s Game of Life for Curved Surfaces - Part 1 - https://news.ycombinator.com/item?id=4808071 - Nov 2012 (1 comment)
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