Theory and Applications of Two-dimensional, Null-boundary, Nine-Neighborhood, Cellular Automata Linear rules

TL;DR

This paper explores 2D cellular automata rules for image processing, classifying them into groups, and introduces a new algorithm applicable to various interdisciplinary problems including image compression, encryption, and pattern classification.

Contribution

It classifies 2D CA linear rules into groups, analyzes their effects on images, and proposes the Sweepers algorithm for diverse applications.

Findings

Uniform rules produce multiple image copies.

Hybrid rules enable zooming, thickening, and thinning effects.

The Sweepers algorithm applies to various interdisciplinary problems.

Abstract

This paper deals with the theory and application of 2-Dimensional, nine-neighborhood, null- boundary, uniform as well as hybrid Cellular Automata (2D CA) linear rules in image processing. These rules are classified into nine groups depending upon the number of neighboring cells influences the cell under consideration. All the Uniform rules have been found to be rendering multiple copies of a given image depending on the groups to which they belong where as Hybrid rules are also shown to be characterizing the phenomena of zooming in, zooming out, thickening and thinning of a given image. Further, using hybrid CA rules a new searching algorithm is developed called Sweepers algorithm which is found to be applicable to simulate many inter disciplinary research areas like migration of organisms towards a single point destination, Single Attractor and Multiple Attractor Cellular Automata Theory, Pattern Classification and Clustering Problem, Image compression, Encryption and Decryption problems, Density Classification problem etc.