2D Moore CA with new boundary conditions and its reversibility

TL;DR

This paper studies 2D Moore cellular automata with mixed boundary conditions, characterizing their rule matrices and identifying conditions for reversibility, advancing understanding of their algebraic properties and potential applications.

Contribution

It provides a new characterization of 2D Moore CA with mixed boundary conditions and establishes criteria for their reversibility, which was not previously explored.

Findings

Characterization of rule matrices under mixed boundary conditions

Conditions for reversibility of 2D Moore CA

Application of rotation to analyze boundary effects

Abstract

In this paper, under certain conditions we consider two-dimensional cellular automata with the Moore neighborhood. Namely, the characterization of 2D linear cellular automata defined by the Moore neighborhood with some mixed boundary conditions over the field $\mathbb{Z}_{p}$ is studied. Furthermore, we investigate the rule matrices of 2D Moore CA under some mixed boundary conditions by applying rotation. Finally, we give the conditions under which the obtained rule matrices for 2D finite CAs are reversible.