Characterization of 2D Cellular Automata with Moore Neighborhood over Ternary Fields

Abstract

A characterization of von Neumann neighborhood cellular automata was extensively studied in the literature. In this paper, we study one of the most commonly used neighborhood types of CA which is called Moore neighborhood in two dimensional lattice. We investigate the characterization of two dimensional Moore neighborhood cellular automata over ternary fields. Moore neighborhood cellular automata over Z(3) corresponds to a new local rule which we called a rule number 9840. By using matrix algebra manipulations, the characterization of 2-dimensional linear cellular automata transformations with periodic and null boundary conditions is explicitly investigated over ternary fields. We also analyze some results about the rule number 9840N.