Definition and Identification of Information Storage and Processing Capabilities as Possible Markers for Turing-universality in Cellular Automata

TL;DR

This paper introduces a method to measure information storage and processing in elementary cellular automata to identify potential universal automata and classify all automata into four complexity-based groups.

Contribution

It proposes a novel approach to quantify information capabilities in cellular automata, linking these features to system complexity and universality potential.

Findings

Classified all elementary cellular automata into four groups

Identified information channels and intersections in cellular automata

Validated that information processing abilities correlate with system complexity

Abstract

To identify potential universal cellular automata, a method is developed to measure information processing capacity of elementary cellular automata. We consider two features of cellular automata: Ability to store information, and ability to process information. We define local collections of cells as particles of cellular automata and consider information contained by particles. By using this method, information channels and channels' intersections can be shown. By observing these two features, potential universal cellular automata are classified into a certain class, and all elementary cellular automata can be classified into four groups, which correspond to S. Wolfram's four classes: 1) Homogeneous; 2) Regular; 3) Chaotic and 4) Complex. This result shows that using abilities of store and processing information to characterize complex systems is effective and succinct. And it is found that these abilities are capable of quantifying the complexity of systems.