Cellular Automata

A 4-state Cellular Automata
A 4-state Cellular Automata

Everything here, unless otherwise noted, is under licensing terms CC BY-NC-SA 4.0, links to and motivation for which you can read here. You may notice use of the "LAB" logo, which I've written an explanation about here.

Before you move on and keep reading, note that all these images were generated entirely automatically by a computer, I did not manually edit any of these after production.

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2 State CA

For cellular automata with two possible states for each cell, there were only 2^(2^3) = 2^8 = 256 possibilities. That's pretty easy for a computer to just auto-generate all of them, so I did that with this code and selected the ones that stood out to me here:

3 State CA

I then expanded to 3 State CA to see if I could yield more complex patterns. However, going up just even one state number increases the possiblities dramatically! There are now 3^(3^3) = 3^27 = 7,625,597,484,987 possible rulesets, generating all of which would take far too long. So I instead randomly generated rulesets, then I picked the ones that stood out to me. I generated using this code.

4 State CA

Just like the 3 State CAs, my motivation was to see whether I could arrive at images with ever-increasing complexities that, although randomly generated, had some structured quality that we could recognize. Once again I did a random search through only some of the possibilities, since there are now an absolutely mindboggling 4^(4^3) = 4^64 = 340,282,366,920,938,463,463,374,607,431,768,211,456 possible rulesets. I generated them using this code.