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arXiv · 0711.1349

Enumeration of number-conserving cellular automata rules with two inputs

Henryk Fuks·Kate Sullivan
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Abstract

We show that there exists a one-to-one correspondence between the set of number-conserving cellular automata (CA) with $q$ inputs and the set of balanced sequences with $q$ terms. This allows to enumerate number-conserving CA. We also show that number-conserving rules are becoming increasingly rare as the number of states increases.

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Henryk Fuks, Kate Sullivan. 2007-11-08. Enumeration of number-conserving cellular automata rules with two inputs. https://arxiv.org/abs/0711.1349

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