Mandelbrot set

mathematics, graphics (After its discoverer, BenoitMandelbrot) 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 Arganddiagram, 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)