Compositions of cellular automata

One way to construct more complicated rules is from compositions of simpler rules. One can, for example, consider each step applying first one elementary cellular automaton rule, then another. The result is in effect a k=2, r=2 rule. Usually the order in which the two elementary rules are applied will matter, and the overall behavior obtained will have no simple relationship to that of either of the individual rules. (See also page 956.)