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There was chaos at the beginning...

Later, after geometry had appeared , mathematicians obviously claimed that it was beautifull, but it still can't explain chaos. Is there any known geometrical figure which could depict clouds, leaves, or dancing dust in the wind, or mop of red hair?

Fractals were discovered quite long ago, but they have been carefully omit-ted, and as a very inconvenient geometrical figure, and treated as a freak of Geometry rather than its phenomena. Nowadays the fractals are mostly defined as automatic (self-repeating) figures. It means, that even the smallest fragments are similar to the whole pattern and could be extended and magnified infinitely.

The term "fractal" was introduced by French matematician and informatician Benoit Mandelbrot in the 70s of XX century. The Mandelbrot set, discovered by him, which looks like that:

didn'd appear to be the first fractal example.
The most popular example sets called "classical fractals" were mainly de-fined in XIX century. Among them there are: the Cantor set, the Koch flake, the Devil's stairs or the Sierpinski triangle.

Personal computer's FLOPS, sufficient for creating more and more beauti-full and detailed fractals, was obtained relatively lately. However nowadays, when I generate a work of rather high resolution printing (ex 2500ˇ2500 pixels), it takes about several hours for Pentium III.

zdrada i podryw fractals of aramin