Rule 110
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Around 2000, Matthew Cook verified a 1985 conjecture by Stephen Wolfram by proving that Rule 110 is Turing complete, i.e., capable of universal computation. Among the 256 possible elementary cellular automata, Rule 110 is the only one for which this 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...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Around 2000, Matthew Cook verified a 1985 conjecture by Stephen Wolfram by proving that Rule 110 is Turing complete, i.e., capable of universal computation. Among the 256 possible elementary cellular automata, Rule 110 is the only one for which this 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 random nor completely repetitive. Localized structures appear and interact in various complicated-looking ways. While working on the development of NKS, Wolfram''s research assistant 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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