On Certain Analytical Representations of Cellular Automata

TL;DR

This paper introduces an extended semi-analytical framework for representing cellular automata dynamics using universal maps and superpotentials, aiming to explore alternative computational models and their physical implications.

Contribution

It generalizes existing representations of cellular automata to arbitrary dimensions and neighborhoods through universal maps and superpotentials, providing new insights into their analytical structure.

Findings

Extended semi-analytical representation of CA dynamics

Unified framework using universal maps and superpotentials

Supports exploration of alternative computational models

Abstract

We extend a previously introduced semi-analytical representation of a decomposition of CA dynamics in arbitrary dimensions and neighborhood schemes via the use of certain universal maps in which CA rule vectors are derivable from the equivalent of superpotentials. The results justify the search for alternative analog models of computation and their possible physical connections.