fractal
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Pronunciation: \ˈfrak-təl\
Etymology: French fractale, from Latin fractus broken, uneven (past participle of frangere to break) + French -ale -al (noun suffix)
Function: noun

1: any of various extremely irregular curves or shapes for which any suitably chosen part is similar in shape to a given larger or smaller part when magnified or reduced to the same size. [1]
A fractal often has the following features:

* It has a fine structure at arbitrarily small scales.
* It is too irregular to be easily described in traditional Euclidean geometric language.
* It is self-similar (at least approximately or stochastically).
* It has a Hausdorff dimension which is greater than its topological dimension (although this requirement is not met by space-filling curves such as the Hilbert curve).
* It has a simple and recursive definition.

Because they appear similar at all levels of magnification, fractals are often considered to be infinitely complex (in informal terms). Natural objects that approximate fractals to a degree include clouds, mountain ranges, lightning bolts, coastlines, and snow flakes. However, not all self-similar objects are fractals—for example, the real line (a straight Euclidean line) is formally self-similar but fails to have other fractal characteristics.[2]

(Vagia Pantou 10.12.2007)
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