(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 ref="module.php?name=Lexikon&file=search&eid=1&query=fractal">fractal - it includes smaller versions of itself which can be explored to arbitrary levels of detail. {The Fractal Microscope (http://www.ncsa.uiuc.edu/Edu/Fractal/Fractal_Start.html/)}. (1995-02-08)
