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From The Free On-line Dictionary of Computing (05 January 2017) [foldoc]:
Mandelbrot set
(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)