An information-theoretic approach to self-organisation: Emergence of complex interdependencies in coupled dynamical systems

TL;DR

This paper introduces an information-theoretic framework to quantify and analyze self-organisation in coupled dynamical systems, revealing how complex interdependencies emerge and can be characterized.

Contribution

It develops a novel theoretical approach using multivariate information theory to measure and decompose self-organisation in dynamical systems, with practical application to cellular automata.

Findings

Identifies a global structural strength metric for self-organisation

Decomposes emergent structures into redundant and synergistic dependencies

Detects complex structures in cellular automata

Abstract

Self-organisation lies at the core of fundamental but still unresolved scientific questions, and holds the promise of de-centralised paradigms crucial for future technological developments. While self-organising processes have been traditionally explained by the tendency of dynamical systems to evolve towards specific configurations, or attractors, we see self-organisation as a consequence of the interdependencies that those attractors induce. Building on this intuition, in this work we develop a theoretical framework for understanding and quantifying self-organisation based on coupled dynamical systems and multivariate information theory. We propose a metric of global structural strength that identifies when self-organisation appears, and a multi-layered decomposition that explains the emergent structure in terms of redundant and synergistic interdependencies. We illustrate our framework on elementary cellular automata, showing how it can detect and characterise the emergence of complex structures.