Elementary cellular automaton Rule 110 explained as a block substitution system Rule 110 as a block substitution system

摘要

This paper presents the characterization of Rule 110 as a block substitution system of three symbols. Firstly, it is proved that the dynamics of Rule 110 is equivalent to cover the evolution space with triangles formed by the cells of the automaton. It is hence demonstrated that every finite configuration can be partitioned in several blocks of symbols and, that the dynamics of Rule 110 can be reproduced by a set of production rules applied to them. The shape of the blocks in the current configuration can be used for knowing the number of them in the next one; with this, the evolution of random configurations, ether and gliders can be modeled.