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.