The blocks needed to represent each cell are now larger, since they must include all 32 cases in the rule. There are also five elimination stages rather than three. But despite these differences, the underlying rule for the universal cellular automaton remains exactly the same.

What about rules that have more than two possible colors for each cell? It turns out that there is a general way of emulating such rules by using rules that have just two colors but a larger number of neighbors. The picture on the facing page shows an example. The idea is that each cell in the three-color cellular automaton is represented by a block of three cells in the two-color cellular automaton. And by looking at neighbors out to distance five on each side, the two-color cellular automaton can update these blocks at each step in direct correspondence with the rules of the three-color cellular automaton.

The same basic scheme can be used for rules with any number of colors. And the conclusion is therefore that the universal cellular automaton can ultimately emulate a cellular automaton with absolutely any set of rules, regardless of how many neighbors and how many colors they may involve.

This is an important and at first surprising result. For among other things, it implies that the universal cellular automaton can emulate cellular automata whose rules are more complicated than its own. If one did not know about the basic phenomenon of universality, then one would most likely assume that by using more complicated rules one would always be able to produce new and different kinds of behavior.

But from studying the universal cellular automaton in this section, we now know that this is not in fact the case. For given the universal cellular automaton, it is always in effect possible to program this cellular automaton to emulate any other cellular automaton, and therefore to produce whatever behavior the other cellular automaton could produce.

In a sense, therefore, what we can now see is that nothing fundamental can ever be gained by using rules that are more complicated than those for the universal cellular automaton. For given the universal cellular automaton, more complicated rules can always be emulated just by setting up appropriate initial conditions.

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