This chapter reviews measures of emergence, self-organization, complexity, homeostasis, and autopoiesis based on information theory. These measures are derived from proposed axioms and tested in two case studies: random Boolean networks and an Arctic lake ecosystem. Emergence is defined as the information produced by a system or process. Self-organization is defined as the opposite of emergence, while complexity is defined as the balance between emergence and self-organization. Homeostasis reflects the stability of a system. Autopoiesis is defined as the ratio between the complexity of a system and the complexity of its environment. The proposed measures can be applied at different scales, which can be studied with multi-scale profiles.

%B Guided Self-Organization: Inception %I Springer %P 19-51 %G eng %U http://arxiv.org/abs/1304.1842 %0 Journal Article %J Entropy %D 2014 %T Measuring the Complexity of Self-organizing Traffic Lights %A Darío Zubillaga %A Geovany Cruz %A Luis Daniel Aguilar %A Jorge Zapotécatl %A Nelson Fernández %A José Aguilar %A David A. Rosenblueth %A Carlos Gershenson %X We apply measures of complexity, emergence, and self-organization to an urban traffic model for comparing a traditional traffic-light coordination method with a self-organizing method in two scenarios: cyclic boundaries and non-orientable boundaries. We show that the measures are useful to identify and characterize different dynamical phases. It becomes clear that different operation regimes are required for different traffic demands. Thus, not only is traffic a non-stationary problem, requiring controllers to adapt constantly; controllers must also change drastically the complexity of their behavior depending on the demand. Based on our measures and extending Ashby's law of requisite variety, we can say that the self-organizing method achieves an adaptability level comparable to that of a living system. %B Entropy %V 16 %P 2384–2407 %G eng %U http://dx.doi.org/10.3390/e16052384 %R 10.3390/e16052384 %0 Journal Article %J Complexity %D 2012 %T Complexity and Information: Measuring Emergence, Self-organization, and Homeostasis at Multiple Scales %A Carlos Gershenson %A Nelson Fernández %X 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. %B Complexity %V 18 %P 29-44 %G eng %U http://dx.doi.org/10.1002/cplx.21424 %R 10.1002/cplx.21424 %0 Conference Paper %B II Simposio Cient{\'ıfico y Tecnológico en Computación SCTC 2012 %D 2012 %T Sistemas Dinámicos como Redes Computacionales de Agentes para la evaluación de sus Propiedades Emergentes. %A Nelson Fernández %A José Aguilar %A Carlos Gershenson %A Oswaldo Terán %B II Simposio Cient{\'ıfico y Tecnológico en Computación SCTC 2012 %C Universidad Central de Venezuela %G eng