# Mandelbrot set

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Related to Mandelbrot spiral: Benoit Mandelbrot, Mandelbrot set

## Mandelbrot set

[¦män·dəl‚bröt ‚set]
(mathematics)
The set of complex numbers, c, for which the sequence s0, s1, … is bounded, where s0=0, and sn+1= sn 2+ c.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

## Mandelbrot set

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

| z[N] | < 2

for arbitrarily large values of N, where

z[0] = 0 z[n+1] = z[n]^2 + c

The 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.