What is a fractal?

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[...] Fractals are typically self-similar patterns, where self-similar means they are "the same from near as from far". [...] The definition of fractal goes beyond self-similarity per se to exclude trivial self-similarity and include the idea of a detailed pattern repeating itself.

Source: Fractal, Wikipedia

Examples

The Rensselaer Polytechnic Institute made an applet which allows you to create fractals by yourself. So I've tried this one as a starter:

You might know this one:

Fractals in Nature

Fractals seem to appear quite often in nature. I have just re-created one that I have seen recently:

Mandelbrot set

The Mandelbrot set is maybe the best known fractal, although it is not a fractal in my opinion. It does never repeat itself.

See also