What is the Mandelbrot set?

The Mandelbrot set is a set of points, a distinctive and easily recognisable two-dimensional fractal shape. It arises from the repeated application of the deceptively simple equation zn+1 = zn2+ C.  Any complex number C, is in the Mandelbrot set if, when starting with z0 = 0 and applying the iteration repeatedly, the absolute value of zn does not head out to infinity.

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