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Complex Systems, Chaos and Fractals

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The last few years have seen an extraordinary growth of interest in Complex Systems. From ecology to economics, from particle physics to parallel computing, from the evolution of life to geophysics, a new vocabulary is emerging to describe discoveries about wide-ranging and fundamental phenomena. Many of the terms have already become familiar: artificial life, biocomplexity, cellular automata, chaos, criticality, fractals, learning systems, neural networks, non-linear dynamics, parallel computation, percolation, self-organization, and many more. Together they point to the emergence of new paradigms, cutting across traditional disciplines, for dealing with complex systems.

There are many sites on the Web where you can find information about Fractals. I recommend the following one: http://www.ncsa.uiuc.edu/Edu/Fractal/Fgeom.html

A self-similar structure commoly found on earth. Its fractal geometry is well developed.

Have you ever wonder why careful geologists always include a scale or reference when taking a picture of geologic interest? The reason is that if they didn't, the actual size or scale of the object pictured could not be determined. This is because most geoforms are self-similar, i.e., a fold 1 cm long looks quite the same as if it is 10 meters or 10 kilometers long. The same with most fault systems, layering, foliations, coastlines, topographic features, drainage patterns like the one above, etc. Self-similarity is a clue to the origin of many physical systems whose internal dynamics may be complex, in the sense that the system is at a critical state between chaos and order; a condition that has been called a self-organized critical state. A very readable account of Self-organized criticality is in the recent book by Per Bak " How Nature Works"

For many years geologists have complained that classical math and physics are too simplistic in their representation of nature to be useful to the geologist. Now there is no more excuse available. Fractal geometry, chaos theory and the science of complex systems do accurately represent many geosystems. Learning about fractals and chaos theory will considerably extend your understanding of geosystems and the workings of nature.

Even evolution is involved...Steve Gould has this to say about fractals and evolution: "Finally, this pattern of long stasis, with change concentrated in rapid episodes that establish new equilibria, may be quite general at several scales of time and magnitude, forming a kind of fractal pattern in self-similarity " (Sc. American, Oct 1994).

This document was prepared by J.A. Rial. (jar@email.unc.edu)