Classification of Cellular Automata based on the Hamming distance

TL;DR

This paper introduces an algorithm that classifies elementary cellular automata using Hamming distance, enhancing Wolfram's phenomenological classification with additional subclasses.

Contribution

The paper presents a novel classification algorithm based on Hamming distance that refines and extends Wolfram's cellular automata categorization.

Findings

Classification aligns with Wolfram's categories

Adds new subclasses to existing classification

Effective in distinguishing automata behaviors

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.