Evolution of cellular automata with conditionally matching rules

This paper introduces a method of representing transition functions for the purposes of evolutionary design of cellular automata. The proposed approach is based on conditions specified in the transition rules that have to be satisfied in order to determine the next state of a cell according to a specific rule. The goal of this approach is to reduce the number of elements needed to represent a transition function while preserving the possibility to specify traditional transition rules known from the conventional table-based representation. In order to demonstrate abilities of the proposed approach, the replication problem and pattern transformation problem in cellular automata will be investigated. It will be shown that the evolution is able to design transition functions for non-trivial behavior of two-dimensional cellular automata that perfectly fulfil the specified requirements.