PERIODICITIES OF SOME HYBRID CELLULAR AUTOMATA WITH RULES 102 AND 60

Abstract

Abstract. We investigate periodicities of some hybrid cellular au-tomata con gured with rule 102 and 60 and null boundary condi-tion. 1. IntroductionCellular automata have been demonstrated by many researchers tobe a good computational model for physical systems simulation sincethe concept of cellular automata rst introduced by John Von Neumannin the 1950’s. And researchers have studied on cellular automata con- gured with rules 51, 60, 102, 153, 195 or 204 [1-7].In this note, we will investigate periodicities of some hybrid cellularautomata con gured with rule 102 and 60 and null boundary condition.2. PreliminariesA cellular automaton (CA) is an array of sites (cells) where eachsite is in any one of the permissible states. At each discrete time step(clock cycle) the evolution of a site value depends on some rule (thecombinational logic) which is a function of the present states of its kneighbors for a k-neighborhood CA. For a 2-state 3-neighborhood CA,the evolution of the (i)th cell can be represented as a function of thepresent states of (i 1)th, (i)th, and (i + 1)th cells as: x