Classification of cellular automata based on the Hamming distance

Gaspar Alfaro; Miguel A F Sanjuán

doi:10.1063/5.0227349

Classification of cellular automata based on the Hamming distance

Chaos. 2024 Aug 1;34(8):083129. doi: 10.1063/5.0227349.

Authors

Gaspar Alfaro¹, Miguel A F Sanjuán¹

Affiliation

¹ Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, Móstoles, 28933 Madrid, Spain.

PMID: 39167772
DOI: 10.1063/5.0227349

Abstract

Elementary cellular automata are the simplest form of cellular automata, studied extensively by Wolfram in the 1980s. He discovered complex behavior in some of these automata and developed a classification for all cellular automata based on their phenomenology. In this paper, we present an algorithm to classify them more effectively by measuring difference patterns using the Hamming distance. Our classification aligns with Wolfram's and further categorizes them into additional subclasses. Finally, we have found a heuristic reasoning providing and explanation about why some rules evolve into fractal patterns.