Generalized Cellular Automata
The number of possible rules, R, for a generalized cellular automaton in which each cell may assume one of S states as determined by a neighborhood size of n, in a D-dimensional space is given by: R=SS(2n+1)D
The most common example has S = 2, n = 1 and D = 1, giving R = 256. It should be noticed that the number of possible rules has an extreme dependence on the dimensionality of the system. For example, increasing the number of dimensions (D) from 1 to 2 increases the number of possible rules from 256 to 2512 (which is ~1.341×10154).
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