Mandelbrot set

Man·del·brot set

M0074425 (män′dəl-brŏt′)n. The set of complex numbers C for which the iteration z_n₊₁ = z_n² + C produces finite z_n 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]

Thesaurus

Noun

$Mandelbrot set - a set of complex numbers that has a highly convoluted fractal boundary when plotted$ 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

[¦män·dəl‚bröt ‚set] (mathematics) The set of complex numbers, c, for which the sequence s₀, s₁, … is bounded, where s₀=0, and s_n+1= s_n²+ 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] = 0z[n+1] = z[n]^2 + c

The Mandelbrot set is usually displayed as an Argand diagram, giving each point a colour which depends on thelargest N for which | z[N] | < 2, up to some maximum N whichis 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 exploredto arbitrary levels of detail.

The Fractal Microscope.

Mandelbrot set

A series of two equations that contain real and imaginary components which, when iterated and plotted on a 2-D graph, depict a highly complex classic fractal pattern. Mandelbrot sets and fractal patterns have been found in branching blood vessels, bronchi and bronchioles, in the heart rate, and in DNA.

Mandelbrot set

Man·del·brot set

Mandelbrot set

Mandelbrot set

Mandelbrot set

Mandelbrot set

Mandelbrot set

Mandelbrot set

Mandelbrot set

Words related to Mandelbrot set

noun a set of complex numbers that has a highly convoluted fractal boundary when plotted

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