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What are fractals?

Why are fractals important?

​"The screen you're staring at right now probably looks like a rectangle.  And the plum I ate this morning was circular. But what if I were to look further, and consider the trees that line the street, the leaves that hang off those trees, the lightning from last night's thunderstorm, the cauliflower I ate for dinner, the blood vessels in my body, and the mountains and coastlines that cover land beyond New York City?  

Most of the stuff you find in nature cannot be described by the idealized geometrical forms of Euclidean geometry." -Daniel Shiffman, "The Nature of Code" (2012)

A fractal is "a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole." -Benoit Mandelbrot, "The Fractal Nature of Geometry" (1975)

Fractals are characterized by self-similarity and  recursion .  They can be generated using the iterated functions systems method.

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