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But one example where there is no such direct analogy is a register machine. And at the outset one might not imagine that such a system could ever readily be emulated by a cellular automaton.

But in fact it turns out to be fairly straightforward to do so, as illustrated at the bottom of the facing page. The basic idea is to have the cellular automaton produce a pattern that expands and contracts on each side in a way that corresponds to the incrementing and decrementing of the sizes of numbers in the first and second registers of

A cellular automaton set up to emulate a sequential substitution system. The cellular automaton involves 28 colors and nearest-neighbor rules. The strings produced by the sequential substitution system appear on successive diagonal stripes indicated by arrows in the evolution of the cellular automaton on the right.

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