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

---

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.

---

Etymology

Origin of Mandelbrot set

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

A good example where you really need the computer is something like the Mandelbrot set.

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