2D Reflexive CA Rules over ℤp

Abstract

The present paper is devoted to study of a new type of lattice that is called pentagonal lattice. We define the von Neumann neighborhood of a cell in this lattice. After that, it is considered a linear Cellular Automata with von Neumann neighborhood over pentagonal lattice. We investigate this Cellular Automata with reflexive boundary condition. For the considered Cellular Automata, we construct the transition rule matrix over the field ℤp with reflexive boundary condition.