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

42 pages, 11 figures, 2 tables

References in corpus (12)

• The structure and function of complex networks
• A Statistical Measure of Complexity
• Computational Mechanics: Pattern and Prediction, Structure and Simplicity
• Restricted Complexity, General Complexity
• Quantifying Self-Organization with Optimal Predictors
• Lyapunov Exponents in Random Boolean Networks
• Complex dynamics of elementary cellular automata emerging from chaotic rules
• The Sigma Profile: A Formal Tool to Study Organization and its Evolution at Multiple Scales
• Computing Networks: A General Framework to Contrast Neural and Swarm Cognitions
• Compression-based investigation of the dynamical properties of cellular automata and other systems
• Quantifying the complexity of random Boolean networks
• Complexity, information transfer and collective behavior in chaotic dynamical networks

Cited by in corpus (18)

• Measuring the Complexity of Urban Form and Design
• Living is information processing: from molecules to global systems
• Measuring the Complexity of Self-organizing Traffic Lights
• An information-theoretic approach to self-organisation: Emergence of complex interdependencies in coupled dynamical systems
• A Novel Antifragility Measure Based on Satisfaction and Its Application to Random and Biological Boolean Networks
• Complexity measurement of natural and artificial languages
• Living in Living Cities
• Behavior of early warnings near the critical temperature in the two-dimensional Ising model
• Emergence in artificial life
• Rank dynamics of word usage at multiple scales
• Antifragility Predicts the Robustness and Evolvability of Biological Networks through Multi-class Classification with a Convolutional Neural Network
• Measuring the Complexity of Continuous Distributions
• Calculating entropy at different scales among diverse communication systems
• Meta-Structures: The Search of Coherence in Collective Behaviours (without Physics)
• Harnessing the Complexity of Education with Information Technology
• A Multilayer Structure Facilitates the Production of Antifragile Systems in Boolean Network Models
• Statistical Properties of Rankings in Sports and Games
• A Categorical Framework for Quantifying Emergent Effects in Network Topology