Enumeration of number-conserving cellular automata rules with two inputs
Henryk Fukś, Sullivan, Kate · arXiv (Cornell University) · 2007
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.