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Finding the Fractals

27 Aug 2009, 22:51 UTC
Finding the Fractals
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Last week NOVA aired a three-part series, Hunting the Hidden Dimension, in which yours truly made a brief cameo appearance. I thought the producers did an excellent job exploring the fascinating hidden world of fractal patterns, and PBS has an excellent affiliated Website set up, wherein you can design your very own fractal.
What exactly are fractals? They arise from chaos theory. To scientists, "chaos" denotes systems that are so sensitive to initial conditions that their output appears random, obscuring their underlying internal rules of order: the stock market, rioting crowds, brain waves during an epilectic seizure, or the weather. In a chaotic system, tiny effects are amplified through repetition until the system goes critical.

The mathematical offspring of chaos theory is fractal geometry. Fractals may appear haphazard at first glance, yet each one is composed of a single geometric pattern repeated thousands of times at different magnifications, like Russian dolls nested within one another. A fractal pattern is what is left behind by chaotic activity. If a hurricane is a chaotic system, then the wreckage strewn in its path is its fractal pattern.

Some fractal patterns exist only in mathematical theory, but
others provide useful models for the ...

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