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I have an interest in cellular automata, of course they make pretty patterns but I am also really interested in the mathematics of them. There can be automata with different grids, different functions, different dimensionality, different domains (countably infinite Vs uncountably grid, finite grids) the à can have non euclidean geometries. Something I am particularly interested in is how and why symmetries and 'conservation laws' occur (e.g time, time reversal, spacial, parity symmetries)
Is there a more general field of mathematics which covers these things (in which I imagine cellular automatas are studied)
Are there any books on this subject, or in cellular automata.
Thank you to everyone who answers
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