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Title: SELF-ORGANIZED CRITICALITY AND CELLULAR AUTOMATA

Abstract

Cellular automata provide a fascinating class of dynamical systems based on very simple rules of evolution yet capable of displaying highly complex behavior. These include simplified models for many phenomena seen in nature. Among other things, they provide insight into self-organized criticality, wherein dissipative systems naturally drive themselves to a critical state with important phenomena occurring over a wide range of length and the scales. This article begins with an overview of self-organized criticality. This is followed by a discussion of a few examples of simple cellular automaton systems, some of which may exhibit critical behavior. Finally, some of the fascinating exact mathematical properties of the Bak-Tang-Wiesenfeld sand-pile model [1] are discussed.

Authors:
Publication Date:
Research Org.:
Brookhaven National Lab. (BNL), Upton, NY (United States)
Sponsoring Org.:
Doe - Office Of Science
OSTI Identifier:
909963
Report Number(s):
BNL-77958-2007-BC
R&D Project: 08775; KA1401020; TRN: US200723%%303
DOE Contract Number:
DE-AC02-98CH10886
Resource Type:
Book
Country of Publication:
United States
Language:
English
Subject:
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; CRITICALITY; DYNAMICS; SAND; STOCKPILES; CALCULATION METHODS

Citation Formats

CREUTZ,M. SELF-ORGANIZED CRITICALITY AND CELLULAR AUTOMATA. United States: N. p., 2007. Web.
CREUTZ,M. SELF-ORGANIZED CRITICALITY AND CELLULAR AUTOMATA. United States.
CREUTZ,M. Mon . "SELF-ORGANIZED CRITICALITY AND CELLULAR AUTOMATA". United States. doi:. https://www.osti.gov/servlets/purl/909963.
@article{osti_909963,
title = {SELF-ORGANIZED CRITICALITY AND CELLULAR AUTOMATA},
author = {CREUTZ,M.},
abstractNote = {Cellular automata provide a fascinating class of dynamical systems based on very simple rules of evolution yet capable of displaying highly complex behavior. These include simplified models for many phenomena seen in nature. Among other things, they provide insight into self-organized criticality, wherein dissipative systems naturally drive themselves to a critical state with important phenomena occurring over a wide range of length and the scales. This article begins with an overview of self-organized criticality. This is followed by a discussion of a few examples of simple cellular automaton systems, some of which may exhibit critical behavior. Finally, some of the fascinating exact mathematical properties of the Bak-Tang-Wiesenfeld sand-pile model [1] are discussed.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Mon Jan 01 00:00:00 EST 2007},
month = {Mon Jan 01 00:00:00 EST 2007}
}

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  • We present a sandpile cellular-automata model that includes the effects of inertia. The model is studied in both one and two dimensions. We find that the model changes the normal self-organized critical behavior, creating a dominance of big events in the system and leading to very large fluctuations in the mass of the system. We show that those changes of behavior can only be noticed in large sandpiles, which is in accord with previous experimental results.
  • Continuous periodogram spectral analyses of global COADS seasonal (Sept.--Nov.) mean surface (air and sea) temperature time series for the 28-year period 1961--1988 show that the spectra follow the universal inverse power law form of the statistical normal distribution. The inverse power law form for power spectra of temporal fluctuations is ubiquitous to real-world dynamical systems and was recently identified as the temporal signature of self-organized criticality. Self-organized criticality implies long range temporal correlations (persistence or memory). The periodogram analyses also give the following results: (1) Periodicities up to 5 years contribute up to 50% of the total variance. (2) Themore » spectra are broad-band with embedded dominant wavebands, the dominant bandwidth increasing with period length. (3) Spiral-like structure of atmospheric flows is seen in the continuous smooth rotation of the phase angle with increase in period length. The above results are consistent with a recently developed nondeterministic cell dynamical system model for atmospheric flows. Identification of a universal spectrum for temperature time series rules out linear secular trends in global surface (air and sea) temperatures The man-made greenhouse gas warming effect will result in energy propagation to all scales of weather and will be manifested immediately in the intensification of high-frequency fluctuations such as the quasi-biennial oscillation (QBO) and El Nino-Southern Oscillation (ENSO) cycles.« less
  • The spatial structure, fluctuations as well as all state probabilities of self-organized (steady) states of cellular automata can be found (almost) exactly and {ital explicitly} from their Markovian dynamics. The method is shown on an example of a natural sand pile model with a gradient threshold. {copyright} {ital 1998} {ital The American Physical Society}
  • We introduce a new nonconservative self-organized critical model. This model is equivalent to a quasistatic two-dimensional version of the Burridge-Knopoff spring-block model of earthquakes. Our model displays a robust power-law behavior. The exponent is not universal; rather it depends on the level of conservation. A dynamical phase transition from localized to nonlocalized behavior is seen as the level of conservation is increased. The model gives a good prediction of the Gutenberg-Richter law and an explanation to the variances in the observed {ital b} values.
  • Cellular automata are the computer scientist's counterpart to the physicist's concept of 'field'. They provide natural models for many investigations in physics, combinatorial mathematics, and computer science that deal with systems extended in space and evolving in time according to local laws. A cellular automata machine is a computer optimized for the simulation of cellular automata. Its dedicated architecture allows it to run thousands of times faster than a general-purpose computer of comparable cost programmed to do the same task. In practical terms this permits intensive interactive experimentation and opens up new fields of research in distributed dynamics, including practicalmore » applications involving parallel computation and image processing. Contents: Introduction. Cellular Automata. The CAM Environment. A Live Demo. The Rules of the Game. Our First rules. Second-order Dynamics. The Laboratory. Neighbors and Neighborhood. Running. Particle Motion. The Margolus Neighborhood. Noisy neighbors. Display and Analysis. Physical Modeling. Reversibility. Computing Machinery. Hydrodynamics. Statistical Mechanics. Other Applications. Imaging Processing. Rotations. Pattern Recognition. Multiple CAMS.« less