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The Mandelbrot set is named after Benoît B. Mandelbrot.The Julia set is named after Gaston Maurice Julia.
Fractals were discovered in 1975 by a scientist names Benoit Mandelbrot.
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The Mandelbrot graph is generated iteratively and so is a function of a function of a function ... and in that sense it is a composite function.
Triangles, spheres, pentagons, cylinders, circles, ellipses, the Mandelbrot Set, etc.