Word:

Mandelbrot set

Noun1.Mandelbrot set - a set of complex numbers that has a highly convoluted fractal boundary when plotted; the set of all points in the complex plane that are bounded under a certain mathematical iteration
(mathematics, graphics)Mandelbrot set - (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 fractal - it includes smaller versions of itself which can be explored to arbitrary levels of detail.

The Fractal Microscope.
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