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)