Enumeration of number-conserving cellular automata rules with two inputs

Details Enumeration of number-conserving cellular automata rules with two inputs Enumeration of number-conserving cellular automata rules with two inputs

2007-11-08

arxiv.org/abs/0711.1349v1

Journal of Cellular Automata 2 vol. 2 pp. 141-148 (2007)

Nonlinear Sciences

Cellular Automata and Lattice Gases

8 pages

Scientific paper

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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