Complexity and Information: Measuring Emergence, Self-organization, and Homeostasis at Multiple Scales

TL;DR

This paper introduces formal information-theoretic measures for complexity, emergence, self-organization, and homeostasis in complex systems, clarifying their meanings through computational experiments on Boolean networks and cellular automata.

Contribution

It proposes concise, formal measures for key complex system concepts, addressing ambiguity and providing a unified framework for analysis.

Findings

Emergence is the opposite of self-organization in the measures.

Complexity is the balance point between emergence and self-organization.

Homeostasis correlates with system stability across scales.

Abstract

Concepts used in the scientific study of complex systems have become so widespread that their use and abuse has led to ambiguity and confusion in their meaning. In this paper we use information theory to provide abstract and concise measures of complexity, emergence, self-organization, and homeostasis. The purpose is to clarify the meaning of these concepts with the aid of the proposed formal measures. In a simplified version of the measures (focusing on the information produced by a system), emergence becomes the opposite of self-organization, while complexity represents their balance. Homeostasis can be seen as a measure of the stability of the system. We use computational experiments on random Boolean networks and elementary cellular automata to illustrate our measures at multiple scales.