Nondeterministic cellular automata

1 February 2023

Written as post ten of #100DaysToOffload.

Yesterday I came across Jan Tewes Thede’s Pixels Fighting. Naturally, I had to look at the source.

I’ve spent many happy hours on cellular automata, but this may be the first one I’ve seen that’s nondeterministic. It uses what might be the canonical rule: a cell is alive in generation \(n + 1\) with probability equal to the proportion of its alive neighbors in generation \(n.\) I remember coding this exact rule in high school, but I used a random initial state instead of the highly ordered one Pixels Fighting uses, which is in my opinion the key to the whole piece.

Searching for “nondeterministic cellular automata” pulls up stuff on the Ising model, which is something I’ve been meaning to read up on for years now. Of course my knowledge of basic physics is woefully incomplete for…some reason, so I’d need a while before tackling statistical mechanics. Hmm…