particular rule, then one will always eventually be able to find a set of localized structures that is rich enough to support universality.

The final demonstration that a given rule is universal will no doubt involve the same kind of elaborate construction as for rule 110.

Examples of cellular automata with class 4 overall behavior, as discussed in Chapter 6. I strongly suspect that all class 4 rules, like rule 110, will turn out to be universal.

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