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by qubex 2241 days ago
I think Stephen Wolfram would beg to differ with you on the topic of how difficult it is to find an ‘interesting la rule – his hole oeuvre (whatever your opinion of the man) demonstrates that these things crop up surprisingly often with even the basest ingredients.

With regards to the kind of rule you speak of, a cellular automata cell in a 3D environment has at most 26 neighbours in the lattice. You could easily increment that to 27 if you wish to make its behaviour depend on its prior state (or even 53 if it you want it to depend on its 26 neighbours’ current state plus 27 prior states of itself and its neighbours). I built such systems (albeit on dynamic networks and 2D automata lattices) for my thesis nigh on 18 years ago. It’s quite utterly trivial.