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But if one allows three possible colors, and requires, say, that the total number of black and gray cells together be conserved, then more complicated behavior can occur, as in the pictures below.

Indeed, as the pictures on the next page demonstrate, such systems can produce considerable randomness even when starting from very simple initial conditions.

Captions on this page:

Block cellular automata with three possible colors which conserve the combined number of black and gray cells. In rule (a), black and gray cells remain in localized regions. In rule (b), they move in fairly simple ways, and in rules (c) and (d), they move in a seemingly somewhat random way. The rules shown here are reversible, although their behavior is similar to that of non-reversible rules, at least after a few steps.

From Stephen Wolfram: A New Kind of Science [citation]