With their simple and rather specific underlying structure one might think that cellular automata would never be capable of emulating a very wide range of other systems.

But knowing that a system like rule 110 is universal, the whole picture changes, and now it seems likely that instead universality should actually be seen in a very wide range of systems, including many with rather simple rules.

But from the Principle of Computational Equivalence there also emerges a new kind of unity: for across a vast range of systems, from

And indeed it is almost inevitable that the scheme will have to be at least somewhat complicated: for if a system is to be universal then it must be able to emulate any of the huge range of other systems that are universal—with the result that specifying which particular such system it is going to emulate for the purposes of a proof will typically require giving a fair amount of information, all of which must somehow be part of the encoding scheme.

But even if a wide range of systems can indeed be shown to be universal this is still not enough to establish the full Principle of Computational Equivalence.

Yet one of the characteristics of the kinds of models based on simple programs that I have developed in this book is that they do appear successfully to capture the computational capabilities of a wide range of systems in nature and elsewhere.

And indeed the Principle of Computational Equivalence implies that a vast range of systems—even ones with very simple underlying rules—should be equivalent in the sophistication of the computations they perform.

But what I have shown in this book is that this is not the case, and that in fact a vast range of systems—including ones with very A two-dimensional cellular automaton that exhibits an almost trivial form of self-reproduction, in which multiple copies of any initial pattern appear every time the number of steps of evolution doubles.

And this means that while the colors of these cells can be updated according to a wide range of different possible rules, the underlying number and organization of cells always stays the same.

But in the long run probably the most important consequence will be to introduce a vast new range of systems and processes that can be used for technology.