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What is the point of the Mandelbrot set?

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The Mandelbrot set is a picture of precisely this dichotomy in the case where 0 is used as the seed. Thus the Mandelbrot set is a record of the fate of the orbit of 0 under iteration of x 2 + c: the numbers c are represented graphically and coloured a certain colour depending on the fate of the orbit of 0.
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