An information-based classification of Elementary Cellular Automata

TL;DR

This paper introduces an information-based classification system for elementary cellular automata that groups rules into classes based on their sensitivity to initial conditions, revealing hierarchical transitions and addressing the origin of complexity.

Contribution

It presents a novel classification method using transfer entropy to categorize cellular automata rules based on their intrinsic complexity and sensitivity to initial states.

Findings

Rules are divided into three classes based on transfer entropy analysis.

Transitions mostly occur within the same class or hierarchically lower classes.

The classification helps distinguish intrinsic complexity from initial state effects.

Abstract

A novel, information-based classification of elementary cellular automata is proposed that circumvents the problems associated with isolating whether complexity is in fact intrinsic to a dynamical rule, or if it arises merely as a product of a complex initial state. Transfer entropy variations processed by the system split the 256 elementary rules into three information classes, based on sensitivity to initial conditions. These classes form a hierarchy such that coarse-graining transitions observed among elementary cellular automata rules predominately occur within each information- based class, or much more rarely, down the hierarchy.