## Mandelbrot set

(After its discoverer, Benoit Mandelbrot) The set of all complex numbers c such that

| z[N] | < 2for arbitrarily large values of N, where

z[0] = 0 z[n+1] = z[n]^2 + cThe Mandelbrot set is usually displayed as an Argand diagram, giving each point a colour which depends on the largest N for which | z[N] | < 2, up to some maximum N which is used for the points in the set (for which N is infinite). These points are traditionally coloured black. The Mandelbrot set is the best known example of a fractal - it includes smaller versions of itself which can be explored to arbitrary levels of detail.

*The Fractal Microscope*.

Last updated: 1995-02-08

### Nearby terms:

Mandelbrot, Benoit ♦ **Mandelbrot set** ♦ mandelbug ♦ Mandy Rice-Davis Applies

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