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I'm currently investigating Wolfram's elementary cellular automata on finite grids with periodic boundary conditions, i.e. on $\mathbb{Z}/k$ for different $k$. It is clear that for each rule $R$ and ...

[Unfortunately, I made some mistakes in my original question. I tacitly corrected them wherever I found them.] Wolfram's rule 18 gives rise to fractal patterns, but when started with two black cells ...

I investigated the long term behaviour of a pair of black cells ■■ on a circle of $N$ cells under the action of each of Wolfram's rules $R$. For each combination $(R,N)$ I determined the first ...

I investigated the evolution of a single black cell on 1-dimensional grids with periodic boundary conditions of variable sizes $N$ under Wolfram's rule 110 which is the only one for which Turing ...