Man·del·brot set  (män'dəl-brŏt')  n. The set of complex numbers C for which the iteration zn+1 = zn2 + C produces finite zn for all n when started at z0 = 0. The boundary of the Mandelbrot set is a fractal. [After Benoit B. Mandelbrot (born 1924), Polish-born American mathematician.] |
| Mandelbrot set (män'dəl-brŏt') Pronunciation Key
The set of complex numbers C for which the iteration zn+1 = zn2 + C produces finite zn for all n when started at z0 = 0. The boundary of the Mandelbrot set is a fractal. |
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.
(1995-02-08)