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Cellular automata

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Cellular automata include:

Some people believe that the universe could be a cellular automaton itself.

The problem with this idea is that the universe, unlike any grid, is isotropic (or appears to be). That must be the reason why you don’t see examples of, for example, circular waves in the whole Wolfram's book or elsewhere. See Cellular Automaton Explorer.

A similar but richer construction is provided by discrete exterior calculus. See also this project: Modeling with discrete exterior calculus about heat transfer.