A-10 2次元セルオートマトンの相転移と結晶化(基礎物理学研究所研究会「複雑系6」報告,研究会報告)

Abstract

The cellular automata (CAs) which lead to uniform regular patterns, namely crystalline CAs are discussed. The two-dimensional and two-states-per-cell CAs with von Neumann neighborhood are particulary focused. First, various CA evolution patterns are analysed by the entropy functions, and it is suggested that there are three types of CAs, i.e. noncrystalline, crysralline and chaotic. Analyses using a newly-introduced rule parameter, called μ, parameter, ensure that the crystalline CAs appear at the phase transition point between noncrystalline and chaotic CAs. The observed phenomena are probably considered as a generalised model of regular-and-static pattern's growth which can be seen in various complex systems.