Mathematics-Online lexicon: Mandelbrot Set

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	Mathematics-Online lexicon:
	Mandelbrot Set

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The Mandelbrot set consists of all points $c=a+\mathrm{i}b \overset{\wedge}{=} (a,b)$ of the complex plane, for which the sequence

defined by

$\displaystyle z_{n+1} = z_n^2 + c,\quad z_0 = 0$

is bounded.

$\includegraphics[width=12cm]{a_mandelbrot_bild.eps}$

In the figure, the speed of a sequence's divergence has been used to define its colour value. Thus the fractal boundary is particularly accentuated.

(Authors: Höllig/Hörner/Kopf/Abele)

Example:

automatically generated 6/11/2007