A Universal Computation Class of Cellular Automata Figure 12 shows patterns obtained by evolution from disordered initial states according to a class 4 cellular automaton rule.
Complicated behavior is evident.
In some cases, however, persistent structures that survive for an infinite time are generated, and a few of these persistent structures propagate with time. Figure 13 shows all the persistent structures generated from initial states with nonzero sites in a region of twenty or fewer sites. Unlike the periodic structures of class 2 cellular automata, these persistent structures have no simple patterns. In addition, the propagating structures allow site values at one position to affect arbitrarily distant sites after a sufficiently long time. No analogous behavior has yet been found in a continuous dynamical system.