Reversibility Algorithm for 2D Cellular Automata with Reflective Condition

Abstract

In the present paper, there are studied main theoretical views of two-dimensional (2D) linear uniform cellular automata with reflective boundary condition over the ternary field, i.e. three states spin case or Z3. We set up a relation between reversibility of cellular automata and characterization of 2D uniform linear cellular automata with this special boundary conditions by using of the matrix theory. In near future, these cellular automata can be found in many different real life applications, e.g. computability theory, theoretical biology, image processing area, textile design, video processing, etc.