Spatial pattern formation in asynchronous cellular automata with mass conservation

This paper proposes a class of two-dimensional asynchronous cellular automata with conservation of mass, for the formation of patterns in groups, and describes the merits given by this methodology. A cellular automaton rule causing a specified kind of pattern was designed manually. Thanks to this realistic modeling method reflecting nature, the mechanism of pattern formation was found to be similar to real chemical processes. Because of the conservation of mass, some “boring” cellular automata which evolve, for instance, into homogeneity are automatically excluded in this scheme. This is greatly advantageous for searching, automatically, for pattern-forming cellular automata. A search technique using genetic algorithm is proposed, and it successfully find a few types of pattern spontaneously, that is, without giving a priori information on the type of pattern. This technique is expected to be applied to a wide range of potential studies related to self-organization.