Mandelbrot set

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Mandelbrot set

[¦män·dəl‚bröt ‚set]
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.
This article is provided by FOLDOC - Free Online Dictionary of Computing (
References in periodicals archive ?
The antenna patch geometry, shown in Figure 1(a), is inspired on the set of Mandelbrot fractals. The Mandelbrot set, graphically, can be divided into an infinite set of cardioids, with the largest of them located at the center of the complex plane.