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yaaqov wrote

This is pretty freaking niche, but I devised a set of tiles (like jigsaw puzzle pieces, basically) that can encode the rules of any elementary 1D cellular automaton (most famously, for instance, rule 110). In these cellular automata, any cell in the grid can be one of two states, “alive” or “dead”, determined by simple, local rules based off the states of neighboring cells; for one of my tiles, little notches on all four sides transfer and store the information about the state of that tile and its neighbors’, and likewise determine the state of its descendent in the time direction.

I’m also working on, but haven’t quite completed, a set of 3D blocks that encode Conway’s game of life, and other totalistic 2D cellular automata: basically the higher-dimensional analog of the above.

One reason I did this and think it’s cool is because these cellular automata are known to be Turing Complete, capable of universal computation and thus “running” any program that any other computer can run, theoretically. In the case of Game of Life, people routinely make beautiful and complex machines and computers in it. By representing these CA as tilings, I’ve sort of proven to myself that a static tiling is capable of computation, just by virtue of its structure, which I just think is a cool thought. Hell, maybe our own universe is an aperiodic tiling! Anyway, I can also draw up a picture to show y’all if anyone wants.

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Bezotcovschina wrote

Anyway, I can also draw up a picture to show y’all if anyone wants.

Please, do. I'm fascinated by cellular automata.

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