Minimal Boolean expression representations for the results of steps 1 through 5 in the evolution of three elementary cellular automata. Both rules 254 and 90 have fairly simple overall behavior, and yield comparatively small Boolean expressions. Rule 30 has much more complicated behavior and yields Boolean expressions whose size grows rapidly from one step to the next. (For steps 1 through 6, the expressions involve 3, 7, 17, 41, 102 and 261 terms respectively.) In each case the Boolean expressions given are the smallest possible in the disjunctive normal form (DNF) used.

Showing Web View For Page 618 Show full page with images