it. A disadvantage of the Wolfram notation, and the use of decimal notation in particular, is that it makes such isomorphisms harder to see than some alternative notations. Despite this, it has become the de facto standard way of referring to one-dimensional cellular automata. 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. 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''). References Cellular automata