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 Mandelbrot set is closely related to the Julia set.
However, domain of convergence of equation (2) for the coefficients {[a.sub.k]} we will also call the Mandelbrot set.
(2004), Fractals nad chaos: the Mandelbrot set and beyond.
The Mandelbrot set (2011), available from: Accessed: 2011-05-13
G.O.D, the 'Generator of Diversity', in the sense used by Churchman (1979, 1982) can be described using the Mandelbrot set. It is an iteration, generating many and diverse irregular shapes, but guided by geometry of basic co-ordinates.
(4) In the animation of a Mandelbrot set the programmed numbers increase or decrease and move outwards or inwards.