experience with computer languages, there is already an indication that the range of systems that are universal might be somewhat broader.

Indeed, Mathematica turns out to be a particularly good example, in which one can pick very different sets of operations to use, and yet still be able to implement exactly the same kinds of programs.

So what about cellular automata and other systems with simple rules? Is it possible for these kinds of systems to be universal?

At first, it seems quite implausible that they could be. For the intuition that one gets from practical computers and computer languages seems to suggest that to achieve universality there must be some fundamentally fairly sophisticated elements present.

But just as we found that the intuition which suggests that simple rules cannot lead to complex behavior is wrong, so also the intuition that simple rules cannot be universal also turns out to be wrong. And indeed, later in this chapter, I will show an example of a cellular automaton with an extremely simple underlying rule that can nevertheless in the end be seen to be universal.

In the past it has tended to be assumed that universality is somehow a rare and special quality, usually possessed only by systems that are specifically constructed to have it. But one of the results of this chapter is that in fact universality is a much more widespread phenomenon. And in the next chapter I will argue that for example it also occurs in a wide range of important systems that we see in nature.

A Universal Cellular Automaton

As our first specific example of a system that exhibits universality, I discuss in this section a particular universal cellular automaton that has been set up to make its operation as easy to follow as possible.

The rules for this cellular automaton itself are always the same. But the fact that it is universal means that if it is given appropriate initial conditions it can effectively be programmed to emulate for example any possible cellular automaton—with any set of rules.

The next three pages [645, 646, 647] show three examples of this.

Exportable Images for This Page:

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