# 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:
 Noun 1 Mandelbrot 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 iterationset - (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 ?
Kilyachkov, Chaldaeva, & Kilyachkov (2018) suggested another method, based on analyzing the structure of the Mandelbrot set of DDM, but there is a need for more careful research of how one can use it.
Among the details are revisiting billiards on the square table, counting periodic orbits, the Mandelbrot set from the inside out, and the entry fee: a crash course in probability theory.
The Mandelbrot set, graphically, can be divided into an infinite set of cardioids, with the largest of them located at the center of the complex plane.
In the article  Giarrusso and Fisher used it for the parameterization of the period 3 hyperbolic components of the Mandelbrot set. Later, in the article , Erkama studied the case of the period 3-4 hyperbolic components of the Mandelbrot set on the (x, y)-plane and completely solved both cases.
The most famous example is probably that this equality holds for the Mandelbrot set. In addition, there are various other situations where box-counting and Hausdorff dimension coincide [35, 36].
What is the connection between the Gilbreath principles of card shuffling and Mandelbrot set? de Bruijn wrote about card shuffling and related the Gilbreath principle to Penrose tiles.
Saupe, 1992, Fractals for the Classroom, Part 2: Complex Systems and Mandelbrot Set, New York: Springer.
Keller, Invariant factors, Julia equivalences and the (abstract) Mandelbrot set, Lecture Notes in Mathematics, 1732, Springer, Berlin, 2000.
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.
Exploiting the actual, prototypal implementation of Sci-[phi] we conducted a preliminary evaluation by developing a program devoted to the computation of the Mandelbrot set and running it both using Sci-[phi] and JJPF.
On Friday at 7 p.m., Movie Night presents "Fractals: The Color of Infinity," about the Mandelbrot Set, a mathematical discovery; a discussion with Finley follows.

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