mandelbrot set

2 definitions found

mandelbrot set - WordNet (r) 2.1 (2005) :

  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

mandelbrot set - Free On-line Dictionary of Computing (26 May 2007) :

  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)