Mandelbrot set

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Related to Mandelbrot set: Julia set, Fractals

Mandelbrot set

[¦män·dəl‚bröt ‚set]
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 ?
As if placed at the centre of the Mandelbrot set, the inhabitant of Gormenghast, the victim of the Trystero system, the messenger in the Imperial Palace of Kafka's parable, the scientist in the force-field tube vainly strive to reach the end of a seemingly finite construct, only to find that in some obscure but perfectly predictable way the structure is endless or grows before them into unsuspected complexities, detours, obstacles--thresholds.
D, the 'Generator of Diversity', in the sense used by Churchman (1979, 1982) can be described using the Mandelbrot set.
History is a Mandelbrot set, as infinitely subdivisible as is space in Zeno's paradox.
Amygdala, a newsletter for people interested in the Mandelbrot Set, includes short articles, reviews of fractal generating software, and a fractal bibliography.
Part IV provides three case studies of the integration of hardware accelerators, including a custom GCD (greatest common divisor) circuit, a Mandelbrot set fractal circuit, and an audio synthesizer based on DDFS (direct digital frequency synthesis) methodology.
He covers complex arithmetic; loci and regions in the complex plane and displaying complex functions; sequences, series, limits, and integrals; harmonic functions, conformal mapping, and some applications; polynomials, roots, the principle of the argument, and Nyquist stability; transforms: Laplace, Fourier, Z, and Hilbert; and fractals and the Mandelbrot set.
The topics are periodic points, chaos in one and two dimensions, systems of differential equations, fractals, creating fractal sets, and complex fractals in Julia sets and the Mandelbrot set.
Fractals for the classroom: Part 2: Complex systems and Mandelbrot set.
AMS-IMS-SIAM Joint Summer Research Conference on Complex Dynamics: 25 years after the Appearance of the Mandelbrot Set (2004: Snowbird, UT)
He has worked to understand the intricate connections of the Mandelbrot set (SN: 11/23/91, p.