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Simulating Experiences: Excursions in Programming. Catastrophes in Complex Systems

Richard J. Gaylord
Organization: University of Illinois at Urbana-Champaign
Department: Department of Material Science and Engineering
Journal / Anthology

Mathematica in Education
Year: 1992
Volume: 2
Issue: 1
Page range: 18-21

The behavior of large systems consisting of many components that have short range interactions is of great theoretical and practical interest. It has recently been proposed (see [Bak, 1991] and [Bak and Chen, 1991]) that the behavior of many complex systems evolves naturally towards a state from which even a small change can cause a chain reaction affecting any number of the system's components and leading to a catastrophe. Once in such a “self-organized critical state”, a system experiences events that are chain reactions of all sizes and durations. In viewing the dynamics of these self-organized critical processes, it has been suggested that fractals are snapshots of the processes and I/f noise is a superposition of the signals produced by the processes (fractal structures and flicker noise are said to be the “spatial and temporal fingerprints of self-organized criticality”) The features of these systems are global in nature and the system moves from one metastable state to another, never reaching equilibrium. These systems are said to be “weakly chaotic”. It has bee suggested that self-organized criticality can account for behavior in many systems, including geology (earthquakes), ecology (species extinction), economy (stock markets), and fluid dynamics (turbulence). Regardless of whether this model is found to be ubiquitous in the behavior of complex systems in general, or even to apply only to a limited number of such systems, it can be used to create some really neat animation graphics.

*Applied Mathematics > Complex Systems
*Mathematics > Discrete Mathematics > Cellular Automata
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