Color Graphs: An Efficient Model For Two-Dimensional Cellular Automata Linear Rules

TL;DR

This paper introduces a novel color graph model for efficiently representing and analyzing all 512 linear rules of two-dimensional nine-neighbor cellular automata, simplifying their study compared to traditional methods.

Contribution

A new color graph-based model for representing all linear rules of 2D cellular automata, providing a simplified analysis framework.

Findings

Color graphs effectively model all 512 linear rules.

Graph properties facilitate easier analysis of cellular automata rules.

The model improves understanding over traditional techniques.

Abstract

Two-dimensional nine neighbor hood rectangular Cellular Automata rules can be modeled using many different techniques like Rule matrices, State Transition Diagrams, Boolean functions, Algebraic Normal Form etc. In this paper, a new model is introduced using color graphs to model all the 512 linear rules. The graph theoretic properties therefore studied in this paper simplifies the analysis of all linear rules in comparison with other ways of its study.