A Survey of Cellular Automata: Types, Dynamics, Non-uniformity and Applications

TL;DR

This survey comprehensively reviews cellular automata, focusing on their types, dynamics, non-uniformity, and diverse applications across scientific fields, highlighting recent developments and practical uses.

Contribution

It provides an extensive overview of cellular automata, emphasizing non-uniform variants and their significance in modeling complex phenomena and solving real-world problems.

Findings

Various types of CAs and their characterization tools

Global behaviors like universality and reversibility

Importance of non-uniform elementary CAs in applications

Abstract

Cellular automata (CAs) are dynamical systems which exhibit complex global behavior from simple local interaction and computation. Since the inception of cellular automaton (CA) by von Neumann in 1950s, it has attracted the attention of several researchers over various backgrounds and fields for modelling different physical, natural as well as real-life phenomena. Classically, CAs are uniform. However, non-uniformity has also been introduced in update pattern, lattice structure, neighborhood dependency and local rule. In this survey, we tour to the various types of CAs introduced till date, the different characterization tools, the global behaviors of CAs, like universality, reversibility, dynamics etc. Special attention is given to non-uniformity in CAs and especially to non-uniform elementary CAs, which have been very useful in solving several real-life problems.