Classification of Cellular Automata based on the Hamming distance

2024/07/08 by Alfaro, Gaspar, Sanjuán, Miguel A. F. · 2 citations
#Cellular Automata and Lattice Gases (nlin.CG) #FOS: Physical sciences

paper · doi:10.48550/arxiv.2407.06175

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.

Cited by

• Phase transition from localization to chaos in classical many-body system
• Counting Short Trajectories in Elementary Cellular Automata using the Transfer Matrix Method

Related

• On the classifiability of cellular automata
• Classification of Cellular Automata Rules Based on Their Properties
• New aspects of symmetry of elementary cellular automata
• An information-based classification of Elementary Cellular Automata
• Bulking II: Classifications of Cellular Automata