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The Notion of Computation | The Significance of Universality in Rule 110


The Significance of Universality in Rule 110

Practical computers and computer languages have traditionally been the only common examples of universality that we ever encounter. And from the fact that these kinds of systems tend to be fairly complicated in their construction, the general intuition has developed that any system that manages to be universal must somehow also be based on quite complicated underlying rules.

But the result of the previous section shows in a rather spectacular way that this is not the case. It would have been one thing if we had found an example of a cellular automaton with say four or five colors that turned out to be universal. But what in fact we have seen is that a cellular automaton with one of the very simplest possible 256 rules manages to be universal.

So what are the implications of this result? Most important is that it suggests that universality is an immensely more common phenomenon than one might otherwise have thought. For if one knew only about practical computers and about systems like the universal cellular automaton discussed early in this chapter, then one would probably assume that universality would rarely if ever be seen outside of systems that were specifically constructed to exhibit it.

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.

A couple of sections ago we discussed the fact that as soon as one has a system that is universal, adding further complication to its rules cannot have any fundamental effect. For by virtue of its universality the system can always ultimately just emulate the behavior that would be obtained with any more complicated set of rules.

So what this means is that if one looks at a sequence of systems with progressively more complicated rules, one should expect that the overall behavior they produce will become more complex only until the threshold of universality is reached. And as soon as this threshold is passed, there should then be no further fundamental changes in what one sees.


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