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Mandelbrot set
(redirected from Mandelbrot sets)

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(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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Not only are mathematical dynamical systems such as fractals and Mandelbrot sets fascinating, but these analyses are being applied to a wide variety of natural physical and biological phenomena, including laser lights, cloud formations, weather patterns, neural networks, and cardiac physiology.
A dynamical systems approach to motor development by Jensen, Jody L. / Physical Therapy
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