# 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.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

## 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 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 ?
However, there are discrepancies between the two approaches (the method of analyzing the structure of the Mandelbrot set and the method of least squares on the sliding interval).
Figure 2 shows the results we measured by computing the Mandelbrot Set on Novello cluster.
At present most frequently were subjected to analysis of two-dimensional polynomial fractals, especially Mandelbrot set, made partial research and testing in this area.
I wrote that the Mandelbrot set constitutes a replica of Gothic space.
For example, one could follow a path looping half-around the Mandelbrot set staying in the region of Cantor sets and one-sided shifts (horseshoes).
What is the geometry of the Mandelbrot set able to tell us about the nature and size of the/a universe?
The sections cover fractals and dimensions, iterative function systems, and the iteration of complex polynomials--Julia sets and the Mandelbrot set. The illustrations use color.
The model for these works is the Mandelbrot set; Stockel believes that if the Minimalists had been familiar with chaos theory, they too might have produced fractals rather than boxes and cubes.
(Just last week I got a Mandelbrot set tattooed on my leg; looks real good.) Mathematics gets a bad rap as being a boring and difficult subject.
A unique set of geometric equations, the Mandelbrot Set, express fractal patterns found in a variety of natural and humanmade objects.
Penrose calls attention to an intricate pattern known as the Mandelbrot set. Generated on computer screens by an absurdly simple formula, this swirling pattern is so complex that successive magnifications of its parts always disclose totally unexpected properties.
Specifically, this article describes a duality between calculation of the Mandelbrot set and calculation of the effects of crosspol jamming on a generic terminal-phase seeker.

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