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To check whether an array list contains only arrangements of colors corresponding to allowed templates one can then use
SatisfiedQ[list_, allowed_] := Apply[And, Map[MatchQ[#, allowed] &, Partition[list, {3, 3}, {1, 1}], {2}], {0, 1}]
2D class 4 cellular automata
No 5- or 9-neighbor totalistic rules nor 5-neighbor outer totalistic ones appear to yield class 4 behavior with a white background.
Planar networks
One feature of a planar network is that it is always possible to identify definite regions or faces bounded by connections in the network.
So what happens when a system one is simulating tries to sample digits in its initial conditions beyond the ones that are stored? The answer depends on the way that arithmetic is handled in the computer system one uses.
… At each step, this map shifts all the base 2 digits in x one position to the left.
But these four classes also have other significant distinguishing features—and one important example of these is their sensitivity to small changes in initial conditions.
And indeed it is a common feature of systems of limited size that the repetition period one sees can depend greatly on the exact size of the system and the exact rule that it follows.
But as soon as an element is formed, one can expect that it will deplete the concentration of the chemical in its local neighborhood, and thus inhibit further elements from forming nearby.
And in addition, one cannot have replacements
Network evolution in which each node is replaced at each step by a fixed cluster of nodes.
And what I discover is that whatever kind of underlying rules one uses, the behavior that emerges turns out to be remarkably similar to the basic examples that we have already seen in cellular automata.
Some of these inputs will be positive if the
Patches generated by a variety of one-dimensional cellular automaton rules.