Tuesday, September 5, 2023

Cellular Automata

I've been interested in CA for many many years, and finally today I wrote my first code that implements the making of 'images' based on one (or possibly several at once) of 256 rules.

...

Well, before I knew it I've gone off the deep end with this stuff.  Making these things that show them 'evolve' is pretty cool, but it looks like there are only a few rules that make anything 'interesting'.  From out of nowhere I go the idea of combining rules.  So take the starting input, apply Rule 1, then use that as input to Rule 2, for input to Rule 3, etc.  I decided to stop at combining three Rules.  This appears to be very very very different than the rule combination on the wolfram website, where it's taking the final results of two different rules and applying xor, or, & and to the images to produce a result.  These results are boring.

The output of one Rule being the input to the next Rule is something I can't find any info on, which means I just haven't found anything yet (likely), or I've come up with something fairly novel.

Here's what combining Rules 86 and 112 look like:



The patterning here is subtle, but if I look at the power spectrum of each row I see this spectacular thing:



Here's the same thing with different starting points:



and the power spectrum:



details of the PS:




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