So what about three-dimensional cellular automata? It is straightforward to generalize the setup for two-dimensional rules to the three-dimensional case. But particularly on a printed page it is fairly difficult to display the evolution of a three-dimensional cellular automaton in a way that can readily be assimilated.
Pages 182 and 183 do however show a few examples of three-dimensional cellular automata. And just as in the two-dimensional case, there are some specific new phenomena that can be seen. But overall it seems that the basic kinds of behavior produced are just the same as in one and two dimensions. And in particular, the basic phenomenon of complexity does not seem to depend in any crucial way on the dimensionality of the system one looks at.