Mandelbrot set

/ 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

Mandelbrot set

/ män′dəl-brŏt′ /

1. 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 z 0 = 0. The boundary of the Mandelbrot set is a fractal.

Word History and Origins

Origin of Mandelbrot set¹

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

Example Sentences

The defining characteristic of a fractal, such as the Mandelbrot set, “is self-similarity,” Dr. Hart said.

From New York Times

Like the Mandelbrot set, the famous fractal icon, the Game of Life inspired the fields of chaos and complexity, which are so similar that I lump them together under a single term: chaoplexity.

From Scientific American

The question sits at the center of Kevin Nguyen’s first novel, “New Waves,” which begins as a workplace caper before spinning out like the fractals in a Mandelbrot set.

From Los Angeles Times

The Mandelbrot set, Julia sets, and all this stuff which would have been impossible to see without a lot of computation and plotting.

From Scientific American

This is how some fractal mathematical objects, such as the Mandelbrot set — a set of complex numbers for which a particular iterated equation does not approach infinity — are generated.

From Nature