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Complexity and information: Measuring emergence, self-organization, and homeostasis at multiple scales

Authors

  • Carlos Gershenson,

    Corresponding author
    1. Departamento de Ciencias de la Computación, Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, A.P. 20-726, 01000 México Distrito Federal México
    2. Centro de Ciencias de la Complejidad, Universidad Nacional Autónoma de México, México
    • Departamento de Ciencias de la Computación, Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, A.P. 20-726, 01000 México Distrito Federal México
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  • Nelson Fernández

    1. Laboratorio de Hidroinformática, Facultad de Ciencias Básicas, Univesidad de Pamplona, Colombia
    2. Centro de Micro-electrónica y Sistemas Distribuidos, Universidad de los Andes, Mérida, Venezuela
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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 article, 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. © 2012 Wiley Periodicals, Inc. Complexity, 2012

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