The set of all complex numbers c such that
| z[N] | < 2for arbitrarily large values of N, where
z[0] = 0 z[n+1] = z[n]^2 + cThe 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.
It was discovered by Benoit B. Mandelbrot who coined the name "fractal" in 1975 from the Latin fractus or "to break".
(08 Feb 1995)