An algorithm embeds any Turing machine into a 1D cellular automaton with linear-time simulation, demonstrated on binary sum, rule 110, and a reversible universal TM.
Mart´ ınez, Andrew Adamatzky, Kenichi Morita, and Maurice Margenstern
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Universal One-Dimensional Cellular Automata Derived for Turing Machines and its Dynamical Behaviour
An algorithm embeds any Turing machine into a 1D cellular automaton with linear-time simulation, demonstrated on binary sum, rule 110, and a reversible universal TM.