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What is the connection between the Mandelbrot set and Julia sets?

April 26, 2017connection julia Mandelbrot

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What is the connection between the Mandelbrot set and Julia sets?

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There is only one Mandelbrot set, but there are an infinity of Julia sets because c can be any complex number. Each point c in the Mandelbrot set specifies the geometric structure of the corresponding Julia set. If c is in the Mandelbrot set, the Julia set will be connected. If c is not in the Mandelbrot set, the Julia set will be a Cantor dust. In other words, the Mandelbrot set is the set of all the values of c for which the corresponding Julia set is connected.