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In Elementary Cellular Automata, rules can show one pattern, but i am wondering if there is something where a cellular automata structure can simulate another structure?

Is there a category for this in Cellular Automata?

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Any cellular automata that could be classified as a universal Turing machine would be able to do this. The Game of Life is one such cellular automata. Here is it (rather pointlessly) simulating itself on a larger scale. Here is a Turing machine implemented in it. This 'category' that you want is probably "cellular automata that qualify as universal Turing machines". I suspect this question will be of interest to you.

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  • $\begingroup$ Welcome! Certainly, any cellular automaton that can simulate a universal Turing machine can simulate other cellular automata. I suppose, though, that it's also possible to have a weaker CA that can simulate other weak CAs, but isn't powerful enough to simulate a universal TM. So the category isn't necessarily just the class of CAs that can simulate universal TMs. $\endgroup$ – David Richerby Mar 9 '16 at 18:24

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