Mandelbrot set


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Related to Mandelbrot set: Julia set, Fractals

Mandelbrot set

[¦män·dəl‚bröt ‚set]
(mathematics)
The set of complex numbers, c, for which the sequence s0, s1, … is bounded, where s0=0, and sn+1= sn 2+ c.

Mandelbrot set

(mathematics, graphics)
(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.
References in periodicals archive ?
The papers from that conference include the indecomposable continua and Julia sets of rational maps, The Henon family, the complex horseshoe locus and real parameter space, Baby Mandelbrot sets, accumulation points of iterated function systems, Siegel disks with boundaries that have only two complementary domains, non-uniform porosity for a subset of some Julia sets, and a summary of open problems.
He has worked to understand the intricate connections of the Mandelbrot set (SN: 11/23/91, p.
The Mandelbrot set is actually quite beautiful when you look at it.
A Java program generated the Mandelbrot set using parallel threads on a multiprocessor system in order to determine the performance benefits of concurrent execution of the threads.
The discovery was featured in the August 1985 issue of Scientific American and the Mandelbrot set became a famous fractal with popular appeal.
The Mandelbrot set serves as a prime example of how simple mathematical operations can yield astonishingly complex geometric forms.
It also has the capacity to meld with Mandelbrot set geometry allowing a comparison of dynamical systems such as the market and economic events that determine security values.
The Mandelbrot set is based on the quadratic equation f(z) = [z.