PERIODICITIES OF SOME ADDITIVE CELLULAR AUTOMATA

Abstract

Abstract. We investigate periodicities of some additive cellular automatawith null boundary condition. 1. IntroductionCellular automata have been demonstrated by many researchers to be agood computational model for physical systems simulation since the concept ofcellular automata rst introduced by John Von Neumann in the 1950’s. Andresearchers have studied on cellular automata con gured with rules 51, 60, 102,153, 195 or 204 [1-8].In this note, we will investigate periodicities of some additive cellular au-tomata with null boundary condition.2. PreliminariesA cellular automaton (CA) is an array of sites (cells) where each site is inany one of the permissible states. At each discrete time step (clock cycle) theevolution of a site value depends on some rule (the combinational logic) which isa function of the present state of its k neighbors for a k-neighborhood CA. Fora 2-state 3-neighborhood CA, the evolution of the i th cell can be representedas a function of the present states of (i 1)