Interesting Properties
Among the 88 possible unique elementary cellular automata, Rule 110 is the only one for which Turing completeness has been proven, although proofs for several similar rules should follow as simple corollaries, for instance Rule 124, where the only directional (asymmetrical) transformation is reversed. Rule 110 is arguably the simplest known Turing complete system.
Rule 110, like the Game of Life, exhibits what Wolfram calls "Class 4 behavior", which is neither completely stable nor completely chaotic. Localized structures appear and interact in various complicated-looking ways.
Matthew Cook proved Rule 110 capable of supporting universal computation. Rule 110 is a simple enough system to suggest that naturally occurring physical systems may also be capable of universality— meaning that many of their properties will be undecidable, and not amenable to closed-form mathematical solutions.
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