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| Mandelbrot Set |
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What is a Fractal?
Fractal - comes from the Latin adjective fractus, which has the same root as fraction or fragment
and means "irregular or fragmented". The stress should logically be on the first syllable, as
in fraction.
In nature, some shapes can often be irregular or fragmented to such an extent that classical
Euclid geometry is incapable of describing their form. No surface using Euclid geometry can
describe the borders of clouds or the rough turbulent seas. This absence of geometric
representation is remedied by using a family of shapes called fractals (in natural patterns
representable by a fractal set). The most useful of these involve chance, and their
irregularities are statistical in nature. One of the most complex examples is that of Brownian
motion, and a brief explanation will follow in the next section.
The appearance of fractal sets differs greatly; descriptions include curves, surfaces or even
clouds of disconnected points. However some fractals are too difficult to put into words that
could truly do justice to its complexity.
Next: Brownian Motion
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