Mandelbrot set

British  

/ ˈmændəlˌbrɒt /

noun

1. 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

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Mandelbrot set Scientific  

/ män′dəl-brŏt′ /

1. The set of complex numbers C for which the iteration z _{n +1} = z _n ² + C produces finite z _n for all n when started at z ₀ = 0. The boundary of the Mandelbrot set is a fractal.

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Etymology

Origin of Mandelbrot set

C20: after Benoît Mandelbrot (1924–2010), French mathematician, born in Poland

Example Sentences

Figure 4.83 The Mandelbrot set is a well-known example of a set of points generated by the iterative chaotic behavior of a relatively simple function.

From Textbooks • Mar. 30, 2016

Figure 34.21 This image is related to the Mandelbrot set, a complex mathematical form that is chaotic.

From Textbooks • Aug. 12, 2015

Visitors can look through a peephole in the wall to see a hidden copy of a 1985 Scientific American issue, which features a colorful picture of the Mandelbrot set on the cover.

From Scientific American • Dec. 21, 2012

The number c is in the Mandelbrot set if 0 is in the filled Julia set of z2+c.

From Scientific American • Sep. 26, 2012

Personally I enjoy the beauty of a Mandelbrot set, and the Fibonacci series - and I am neither mathematician nor artist, but a botanist & computer scientist.

From BBC • Mar. 5, 2010