Binary States Cellular Automata with Reflexive and Periodic Boundaries and Image problem

Abstract

The present paper focuses on the theory of two-dimensional (2D) linear cellular automata (CA) withrespect to uniform reflexive and periodic boundary conditions. It is investigated the theoretical aspects of 2D linearCA over binary states field with image problem. We consider geometrical and visual aspects of images generatedby these CA transition rules. Multiple copies of any arbitrary images corresponding to CA can be studied furtherby considering theses transition rules of von Neumann and Moore CAs. An important note that these special typesof CAs can be applied many different special problems e.g. computability theory, applied mathematics, theoreticalchemistry and biology, DNA and genetics research, image science, textile design.