Program verifying solution formulae for ternary CA induced by semigroups
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Abstract
Program for verifying solution formulae for 18 cellular automata induced by semigroups, as listed in the paper "Ternary cellular automata induced by semigroups of order 3 are solvable", Proceedings of AUTOMATA 2025.
Description
This program produces spatio-temporal patterns for any of the 18 ternary CA rules induced by semigroups. User needs only to change the number in the line "rule=number", the number must be 1 to 18. Numbers are the same as in the paper "Ternary cellular automata induced by semigroups of order 3 are solvable". The output consists of three pictures:
(1) pattern generated by the CA rule by normal iterations;
(2) the same pattern generated from the solution formula;
(3) the difference between them (should be empty - all white).