On Routine Evolution of Complex Cellular Automata

This paper discusses a special technique, called conditionally matching rules (CMRs), for the representation of transition functions of cellular automata (CA) and its application to the evolutionary design of complex multistate CA. The problem of designing replicating loops in 2-D CA and the square calculation in 1-D CA will be treated as case studies. It will be shown that the evolutionary algorithm in combination with CMRs is able to successfully solve these tasks and provide some innovative results compared to existing solutions. In particular, a novel replication scheme will be presented that exhibits a higher replication speed in comparison with the existing replicating loops. As regards the square calculation, some results have been obtained that allow a substantial reduction of the number of steps of the cellular automaton against the currently known solution. The utilization of the CMRs in the proposed experiments represents the first case of a successful automatic evolutionary design of complex CA for solving nontrivial problems in which the existing conventional approaches have failed.