Mandelbrot set

from WordNet (r) 3.0 (2006)

Mandelbrot set
    n 1: a set of complex numbers that has a highly convoluted
         fractal boundary when plotted; the set of all points in the
         complex plane that are bounded under a certain mathematical
         iteration

from The Free On-line Dictionary of Computing (8 July 2008)

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
   (http://ncsa.uiuc.edu/Edu/Fractal/Fractal_Home.html/).

   (1995-02-08)