Examples of cellular automata with rules of varying complexity. The rules used are of the so-called totalistic type described on page 60. With two possible colors, just 4 cases need to be specified in such rules, and there are 16 possible rules in all. But as the number of colors increases, the rules rapidly become more complex. With three colors, there are 7 cases to be specified, and 2187 possible rules; with five colors, there are 13 cases to be specified, and 1,220,703,125 possible rules. But even though the underlying rules increase rapidly in complexity, the overall forms of behavior that we see do not change much. With two colors, it turns out that no totalistic rules yield anything other than repetitive or nested behavior. But as soon as three colors are allowed, much more complex behavior is immediately possible. Allowing four or more colors, however, does not further increase the complexity of the behavior, and, as the picture shows, even with five colors, simple repetitive and nested behavior can still occur.
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