2D periodic CA rules over $\mathbb{Z}_{2}$ and applications of image processing

Abstract

This work deals with the theory 2-dimensional (2D), uniform periodic boundary replications cellular automata (2D PB CA) of linear rules with applications of image processing science. We investigate a 2D CA with PB over the binary field $\mathbb{Z}_{2}$ case, i.e. 2-state spin case. It is also studied image applications corresponding for the linear (additive) rules of uniform 2D CA PB over binary field (two-states) $\mathbb{Z}_{2}$.