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The details for any particular case are quite complicated, but in the end it turns out that it is in principle possible to construct a cellular automaton that emulates a practical computer in its entirety.

And as a result, one can conclude that any of the very wide range of computations that can be performed by practical computers can also be done by cellular automata.

From the previous section we know that any cellular automaton can be emulated by a universal cellular automaton. But now we see that a universal cellular automaton is actually much more universal than we saw in the previous section. For not only can it emulate any cellular automaton: it can also emulate any of a wide range of other systems, including practical computers.

Captions on this page:

A cellular automaton set up to emulate random-access memory in a computer. The memory is on the right, and can be of any size. Instructions come in from the left, with memory locations specified by addresses consisting of binary digits.

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