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Wikipedia Description

The Mandelbrot set is the set of complex numbers c for which the function does not diverge when iterated from, i.e., for which the sequence, , etc., remains bounded in absolute value.The set is closely related to the idea of Julia sets, which produce similarly complex shapes. Its definition and name are due to Adrien Douady, in tribute to the mathematician Benoit Mandelbrot.Mandelbrot set images are made by sampling complex numbers and determining for each whether the result tends towards infinity when a particular mathematical operation is iterated on it. Treating the real and imaginary parts of each number as image coordinates, pixels are colored according to how rapidly the sequence diverges, if at all.More precisely, the Mandelbrot set is the set of values of c in the complex plane for which the orbit of 0 under iteration of the quadratic mapremains bounded. That is, a complex number c is part of the Mandelbrot set if, when starting with z0 = 0 and applying the iteration repeatedly, the absolute value of zn remains bounded however large n gets. This can also be represented as