Mandelbrot set

The Mandelbrot set is a set of points in the complex plane that forms a fractal. Mathematically, the Mandelbrot set can be defined as the set of complex c-values for which the orbit of 0 under iteration of the complex quadratic polynomial x2 + c remains bounded.The Mandelbrot set has become popular outside mathematics both for its aesthetic appeal and for being a complicated structure arising from a simple definition. Benoît Mandelbrot and others worked hard to communicate this area of mathematics to the public.
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Noun
1. 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
(hypernym) set

<mathematics, graphics> (After its discoverer, Benoit Mandelbrot) The set of all complex numbers c such that
| z[N] |  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] | fractal - it includes smaller versions of itself which can be explored to arbitrary levels of detail.
The Fractal Microscope.
(1995-02-08)