Mandelbrot set


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Related to Mandelbrot set: Julia set, Fractals

Man·del·brot set

 (män′dəl-brŏt′)
n.
The set of complex numbers C for which the iteration zn+1 = zn2 + C produces finite zn for all n when started at z0 = 0. The boundary of the Mandelbrot set is a fractal.

[After Benoit B. Mandelbrot (1924-2010), Polish-born American mathematician.]

Mandelbrot set

(ˈmændəlˌbrɒt)
n
(Mathematics) maths a set of points in the complex plane that is self-replicating according to some predetermined rule such that the boundary of the set has fractal dimensions, used in the study of fractal geometry and in producing patterns in computer graphics
[C20: after Benoît Mandelbrot (1924–2010), French mathematician, born in Poland]
ThesaurusAntonymsRelated WordsSynonymsLegend:
Noun1.Mandelbrot set - a set of complex numbers that has a highly convoluted fractal boundary when plottedMandelbrot set - 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
set - (mathematics) an abstract collection of numbers or symbols; "the set of prime numbers is infinite"
Translations

Mandelbrot set

[ˈmændəlˌbrɒtˌset] N (Math) → conjunto m de Mandelbrot

Mandelbrot set

n (Math) → Mandelbrotmenge f
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References in periodicals archive ?
Saupe, 1992, Fractals for the Classroom, Part 2: Complex Systems and Mandelbrot Set, New York: Springer.
De Bruijn sequences, the Gilbreath Principle (which lets the spectator shuffle a normal deck of cards with them still staying in an order that the magician can predict) and their connection with the Mandelbrot set (identical patterns that make up a larger identical pattern) are discussed in some detail and their applications in magic tricks dealt with.
Movie Night presents "Fractals: The Color of Infinity," about the Mandelbrot Set, a mathematical discovery; a discussion with Finley follows.
Covering in turn real dynamics and complex dynamics, they consider such topics as directional entropies of cellular automaton-maps, a monotonicity conjecture for real cubic maps, self-similarity and hairiness in the Mandelbrot set, the Fibonacci unimodal map, and the mathematical work of Curt McMullen.
The system is based on polynomial fractal sets, specifically on the Mandelbrot set.
The real interval [-2, 1/4] is the real part of the Mandelbrot set for the family [Q.
For example, one may well argue that "five" (the abstract quantity, fiveness) exists apart from us--even if humans had never evolved, you could still have five rocks in a field--and perhaps this extends to fractions and even irrational numbers; but when you start to talk about negative numbers, complex numbers, hypercomplex numbers, infinitesimals, transfinites, matrices, vectors, multi-variable functions, tensors, fields, Galois groups, and the Mandelbrot set the compulsion to regard these as purely mental constructs is overwhelming.
Visualizations of the Mandelbrot Set, the Lorenz Attractor and the Feigenbaum function in the complex plane are stunning and rival many renditions of what are considered more conventional art forms.
The sections cover fractals and dimensions, iterative function systems, and the iteration of complex polynomials--Julia sets and the Mandelbrot set.