Definitions for mandelbrot set
man·del·brot set

Princeton's WordNetRate this definition:0.0 / 0 votes

1. Mandelbrot setnoun

   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 iteration

WiktionaryRate this definition:0.0 / 0 votes

1. Mandelbrot setnoun

   the set of complex numbers c for which the orbit of 0 under iteration of the complex quadratic polynomial z = z + c remains bounded. The boundary of this set is a fractal.

ChatGPTRate this definition:0.0 / 0 votes

1. mandelbrot set

   The Mandelbrot set is a collection of points in the complex plane, the boundary of which forms a fractal. Mathematically, the Mandelbrot set is defined as the set of points c in the complex plane for which the iteratively defined sequence z_{n+1} = (z_n)^2 + c, with z_0 = 0, stays bounded. In other words, if the series of z does not diverge after a certain number of steps, then c is a member of the Mandelbrot set. The set is named after Benoit Mandelbrot, a French-American mathematician who extensively studied fractals.

WikidataRate this definition:0.0 / 0 votes

1. Mandelbrot set

   The Mandelbrot set is a mathematical set of points whose boundary is a distinctive and easily recognizable two-dimensional fractal shape. The set is closely related to Julia sets, and is named after the mathematician Benoit Mandelbrot, who studied and popularized it. Mandelbrot set images are made by sampling complex numbers and determining for each whether the result tends towards infinity when a particular mathematical operation is iterated on it. Treating the real and imaginary parts of each number as image coordinates, pixels are colored according to how rapidly the sequence diverges, if at all. More precisely, the Mandelbrot set is the set of values of c in the complex plane for which the orbit of 0 under iteration of the complex quadratic polynomial zn+1 = zn² + c remains bounded. That is, a complex number c is part of the Mandelbrot set if, when starting with z0 = 0 and applying the iteration repeatedly, the absolute value of zn remains bounded however large n gets. For example, letting c = 1 gives the sequence 0, 1, 2, 5, 26,…, which tends to infinity. As this sequence is unbounded, 1 is not an element of the Mandelbrot set. On the other hand, c = −1 gives the sequence 0, −1, 0, −1, 0,…, which is bounded, and so −1 belongs to the Mandelbrot set.

Matched Categories

1. • Set

How to pronounce mandelbrot set?

1. Alex

   US English

   David

   US English

   Mark

   US English

   Daniel

   British

   Libby

   British

   Mia

   British

   Karen

   Australian

   Hayley

   Australian

   Natasha

   Australian

   Veena

   Indian

   Priya

   Indian

   Neerja

   Indian

   Zira

   US English

   Oliver

   British

   Wendy

   British

   Fred

   US English

   Tessa

   South African

How to say mandelbrot set in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of mandelbrot set in Chaldean Numerology is: 4

2. Pythagorean Numerology

   The numerical value of mandelbrot set in Pythagorean Numerology is: 4

References

1. ^ Princeton's WordNet
   http://wordnetweb.princeton.edu/perl/webwn?s=mandelbrot set
2. ^ Wiktionary
   https://en.wiktionary.org/wiki/Mandelbrot_Set
3. ^ ChatGPT
   https://chat.openai.com
4. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=mandelbrot set