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[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'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 ...

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 ...

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 ...