Numerous variants on the theme of cellular automata have been proposed, such as stochastic evolutionary rules, varying the rule from one cell to another or from time to time, or even permitting such variations in the definitions of the neighborhoods. Unfortunately the quantity of computation required to simulate an automaton increases exponentially, and usually with a rather large exponent, with the size of the parameters involved. Thus any increase in the number of parameters will only aggravate a situation which is already rather difficult. If a significant practical application of one of these variants were to be discovered, no doubt the means would be found to compute its properties. In the meantime the regular version of cellular automata has enough unsolved problems to keep one occupied.
There are two visible tendencies. One is the approach of Conway, or of those who already have an automaton and want to find out what it does. The other is the original approach of von Neumann, to go ahead and construct the automaton which one requires, regardless of the cost in cells and states. Given that a Turing machine can be embedded in cellular automata in a fairly standard way, there will always be some automaton which will realize a given calculation; typically such a straightforward realization will be neither aesthetic nor efficient.
In either event enormous computer power is required. In the former, the de Bruijn diagrams are enormous; for two dimensional binary automata, it is hardly even possible to compute the period 2 states for Life , for instance. For one dimensional binary nearest neighbor automata, the calculation of cycles of length 34 or periods of length 15 strain present microcomputer capacity. Yet computer experiments reveal numerous configurations which are even bigger or repeat with longer periods. So, although much surer, systematic computation does not yet extend to revealing many fairly common experimental results.
Self consistent probabilities likewise require exponentially growing facilities, as the number of nonlinear equations to be solved increases with order. In the second case these concerns may be set aside, but it is still necessary to manage an extremely large table of transitions and to ensure its own internal consistency, especially in the face of backtracking from changed decisions as the rule is gradually elaborated.