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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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