CHARACTERISTIC MATRICES OF CELLULAR AUTOMATA WITH RULE 60 AND INTERMEDIATE BOUNDARY CONDITION

Abstract

Abstract. We investigate periodicities of characteristic matricesof cellular automata con gured with rule 60 and intermediate bound-ary condition. 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 some researchers have studied on cellular automatawith intermediate boundary condition [1,2,4,5,7].In this note, we will investigate periodicities of characteristic matricesof cellular automata con gured with rule 60 and intermediate boundarycondition.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