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Elementary Cellular Automata as Multiplicative Automata

Published 19 Feb 2025 in nlin.CG and cs.DM | (2502.13360v1)

Abstract: Elementary cellular automata (ECA) are converted into multiplicative versions by using permuted n-dim Galois fields and octonion multiplication tables as binary pointers to each rule's Wolfram code truth table. This enables an extension of the binary ECA to complex numbers, identity solutions are found, produces a polynomial, and is implemented in Java.

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