2D mobile automata
Mobile automata can be generalized just like Turing machines. Even in the simplest case, however, with only four neighbors involved there are already (4k)k5
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\!\(\*SuperscriptBox[\((4k)\),\(\!\(\*SuperscriptBox[\(k\),\(5\)]\)\)]\) possible rules, or nearly 1029 even for k = 2
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k = 2.