Definition of the Subject
Self-organized criticality is a concept invoked to explain the frequent occurrence of fractal structures and multi-scale phenomenain nature. In contrast with the ideas of chaos, here simple common features appear in systems with many degrees of freedom. For modeling thisphenomenon, cellular automata provide an elegant class of dynamical systems which are easily simulated numerically.
Introduction
Cellular automata provide a fascinating class of dynamical systems based on very simple rules of evolution yet capable of displaying highlycomplex behavior. These include simplified models for many phenomena seen in nature. Among other things, they provide insight into self-organizedcriticality, wherein dissipative systems naturally drive themselves to a critical state with important phenomena occurring over a wide range oflength and time scales.
This article begins with an overview of self-organized criticality. This is followed by a discussion of a few examples of...
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Abbreviations
- Abelian group :
-
AÂ mathematical group wherein all the elements commute.
- Avalanche :
-
A possibly large disturbance induced in a system by a small perturbation.
- Cellular automaton :
-
This refers to the dynamics of a collection of cells each of which can be in a finite set of states. The evolution is discrete, with the state of a cell at the next time step being dependent only on its previous state and that of its neighbors.
- Chaos :
-
The tendency of a system of a few degrees of freedom to exhibit highly erratic behavior characterized by an infinite range of time scales.
- Self-organized criticality:
-
The tendency of certain discrete and dissipative dynamical systems to evolve to a state where changes occur over all possible length scales.
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Acknowledgments
I am thankful for discussions with many people, but most particularly P. Bak, D. Dar, E. Fredkin, N. Margolis, M. Paczuski, T. Toffoli,F. Van Scoy, and G. Vichniac. This manuscript has been authored under contract number DE-AC02-76CH00016 with the US Department of Energy.Accordingly, the US Government retains a non-exclusive, royalty-free license to publish or reproduce the published form of thiscontribution, or allow others to do so, for US Government purposes.
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Creutz, M. (2009). Self-organized Criticality and Cellular Automata. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, New York, NY. https://doi.org/10.1007/978-0-387-30440-3_474
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