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Self-organized Criticality and Cellular Automata

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Computational Complexity

Article Outline

Glossary

Definition of the Subject

Introduction

Self-Organized Criticality

Cellular Automata

The Sandpile Revisited

Future Directions

Acknowledgments

Bibliography

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Abbreviations

Abelian group :

A 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.

Bibliography

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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.

Author information

Authors and Affiliations

  1. Physics Department, Brookhaven National Laboratory, Upton, USA

    Michael Creutz

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  1. Michael Creutz
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Editor information

Editors and Affiliations

  1. RAMTECH LIMITED, 122 Escalle Lane, Larkspur, CA, 94939, USA

    Robert A. Meyers Ph. D. (Editor-in-Chief) (Editor-in-Chief)

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Creutz, M. (2012). Self-organized Criticality and Cellular Automata. In: Meyers, R. (eds) Computational Complexity. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1800-9_171

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