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.

Last updated: 1995-02-08

Nearby terms:

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

Try this search on Wikipedia, Wiktionary, Google, OneLook.

Loading