(maths) a set of points in the complex plane that is self-replicating according to some predetermined rule such that the boundary of the set has fractal dimensions, used in the study of fractal geometry and in producing patterns in computer graphics
Word Origin
C20: after Benoît Mandelbrot (1924–2010), French mathematician, born in Poland
(män'dəl-brŏt') The set of complex numbers C for which the iteration z_{n}_{+1} = z_{n}^{2} + C produces finite z_{n} for all n when started at z_{0} = 0. The boundary of the Mandelbrot set is a fractal.
mathematics, graphics (After its discoverer, Benoit Mandelbrot) The set of all complex numbers c such that | z[N] | 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] | 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)