Zbiór Mandelbrota (żuk Mandelbrota) – podzbiór płaszczyzny zespolonej, którego brzeg jest jednym ze sławniejszych fraktali. Nazwa tego obiektu została wprowadzona dla uhonorowania jego odkrywcy, francuskiego matematyka Benoit Mandelbrota.

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  • De Mandelbrotverzameling is een fractal die een belangrijke rol speelt in de chaostheorie. De verzameling is genoemd naar Benoît Mandelbrot, een Pools-Franse wiskundige die de fractal in 1980 voor het eerst met de behulp van een computer onderzocht. De verzameling werd echter al in 1905 onderzocht door Pierre Fatou, een Franse wiskundige die zich specialiseerde in de studie van recursieve vergelijkingen.Buiten de chaostheorie staat de Mandelbrotverzameling vooral bekend om zijn esthetische eigenschappen en is daarom vaak het onderwerp van recreatieve wiskunde en inleidende cursussen in fractals.
  • Zbiór Mandelbrota (żuk Mandelbrota) – podzbiór płaszczyzny zespolonej, którego brzeg jest jednym ze sławniejszych fraktali. Nazwa tego obiektu została wprowadzona dla uhonorowania jego odkrywcy, francuskiego matematyka Benoit Mandelbrota.
  • マンデルブロ集合(マンデルブロしゅうごう、Mandelbrot set)とは、 複素平面上の集合、またはそれを複素平面上にプロットしたフラクタル図形。
  • 망델브로 집합(영어: Mandelbrot set)은 브누아 망델브로가 고안한 프랙탈의 일종이다.
  • 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 (which include similarly complex shapes) 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 polynomialremains 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.Images of the Mandelbrot set display an elaborate boundary that reveals progressively ever-finer recursive detail at increasing magnifications. The "style" of this repeating detail depends on the region of the set being examined. The set's boundary also incorporates smaller versions of the main shape, so the fractal property of self-similarity applies to the entire set, and not just to its parts.The Mandelbrot set has become popular outside mathematics both for its aesthetic appeal and as an example of a complex structure arising from the application of simple rules, and is one of the best-known examples of mathematical visualization.
  • Mandelbrot kümesi, Benoit Mandelbrot'un ikinci derece kompleks değişkenli polinomların dinamiklerini açıklamak için geliştirdiği ve incelediği kümedir. Mandelbrot kümesi, karmaşık düzlemin bir fraktal altkümesidir.
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  • Zbiór Mandelbrota (żuk Mandelbrota) – podzbiór płaszczyzny zespolonej, którego brzeg jest jednym ze sławniejszych fraktali. Nazwa tego obiektu została wprowadzona dla uhonorowania jego odkrywcy, francuskiego matematyka Benoit Mandelbrota.
  • マンデルブロ集合(マンデルブロしゅうごう、Mandelbrot set)とは、 複素平面上の集合、またはそれを複素平面上にプロットしたフラクタル図形。
  • 망델브로 집합(영어: Mandelbrot set)은 브누아 망델브로가 고안한 프랙탈의 일종이다.
  • Mandelbrot kümesi, Benoit Mandelbrot'un ikinci derece kompleks değişkenli polinomların dinamiklerini açıklamak için geliştirdiği ve incelediği kümedir. Mandelbrot kümesi, karmaşık düzlemin bir fraktal altkümesidir.
  • 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 (which include similarly complex shapes) 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.
  • De Mandelbrotverzameling is een fractal die een belangrijke rol speelt in de chaostheorie. De verzameling is genoemd naar Benoît Mandelbrot, een Pools-Franse wiskundige die de fractal in 1980 voor het eerst met de behulp van een computer onderzocht.
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  • Ensemble de Mandelbrot
  • Conjunt de Mandelbrot
  • Conjunto de Mandelbrot
  • Conjunto de Mandelbrot
  • Insieme di Mandelbrot
  • Mandelbrot kümesi
  • Mandelbrot set
  • Mandelbrot-Menge
  • Mandelbrot-halmaz
  • Mandelbrotova množina
  • Mandelbrotverzameling
  • Zbiór Mandelbrota
  • Множество Мандельброта
  • マンデルブロ集合
  • 망델브로 집합
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