Apr 19
32 megapizel butterfly fractal (4-fold recursive formula) generated in 46 seconds in python on 20% of an Intel Core i5-8600K @ 3.60 GHz.
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32 megapizel butterfly fractal (4-fold recursive formula) generated in 46 seconds in python on 20% of an Intel Core i5-8600K @ 3.60 GHz.
sierpinski gasket variant
detail B4=MOD(A3+A2+B1+C2+C3,3)
Warp is a hybrid of skip and launch. It uses Launch's "fuel" behavior, but upon leaving friendly territory it spends all its fuel at once to teleport that many pixels straight ahead.
combining random elementary cellular automate rules
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Stills from a Sum of Neighbours cellular automaton on a grid of triangles. Animation only available at Patron.
The rule used—that I call rule 30—is of exactly the same kind as before, and can be described as follows. First, look at each cell and its right-hand neighbor. If both of these were white on the previous step, then take the new color of the cell to be whatever the previous color of its left-hand neighbor was. Otherwise, take the new color to be the opposite of that.
The picture shows what happens when one starts with just one black cell and then applies this rule over and over again. And what one sees is something quite startling—and probably the single most surprising scientific discovery I have ever made. Rather than getting a simple regular pattern as we might expect, the cellular automaton instead produces a pattern that seems extremely irregular and complex.
But where does this complexity come from? We certainly did not put it into the system in any direct way when we set it up. For we just used a simple cellular automaton rule, and just started from a simple initial condition containing a single black cell. —Stephen Wolfram, A New Kind of Science
“Molecule Shoes” by Francis Bitonti. Designed using cellular automata, then 3D-printed. Mathematics is fashionable!
Mathematics is beautiful. <3
Cellular automata are really interesting: Through the interplay of simple rules emerges fairly complex behavior, sometimes capable of universal computation.
They can also look really pretty: A few days ago, I came across some 1D cellular automata posters on Reddit. Sadly, the available images were way too tiny for printing and the author hasn’t yet posted the "high res print exports" supposedly "available soon" – so I took matters into my own hands by writing a poster generator in Python. With the help of Cairo, it generates arbitrarily scalable PDFs whose look is fairly customizable – the images above are screenshots of the generated PDFs.
The cellular automata poster generator is available on GitHub, along with setup instructions, examples and a list of potential future work.