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The pictures below show how a cellular automaton can evaluate any logic expression that is given in a certain form. And the picture on the facing page then shows how a cellular automaton can retrieve data from a numbered location in what is effectively a random-access memory.

Captions on this page:

A cellular automaton which emulates basic logic circuits. The underlying rules for the cellular automaton are exactly the same in each case, and involve nearest neighbors and five possible colors for each cell. But the initial condition can represent a logic expression that involves any number of variables together with the operations of And, Or and Not. In the examples above, two variables, p and q, are used, and in each case the behavior obtained with all four possible combinations of values for p and q are shown.

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