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What are fractals?

What are fractals? Here are some definitions.

Noun
  1. plural of fractal
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Examples
He showed how fractals can occur in many different places in both mathematics and elsewhere in nature.
Strange attractors have detailed structure on all scales of magnification and were one of the early fractals to be studied.
He noted that the body is full of fractals, self-similar repeating patterns at different scales, just as nature is full of fractals.
Of course, no class on maths and the visual arts would be complete without fractals.
All of these elements are combined into seemingly aleatory compositions that, like fractals, operate on several scales at once.
Some of the complexity has been captured in modern pictures of fractals, many of which are created by iterating functions of this kind.

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