The Mandelbrot set (/ˈmændəlbroʊt, -brɒt/) is a two-dimensional set that is defined in the complex plane as the complex numbers c {\displaystyle c} for...

Benoit B. Mandelbrot (20 November 1924 – 14 October 2010) was a Polish-born French-American mathematician and polymath with broad interests in the practical...

There are many programs and algorithms used to plot the Mandelbrot set and other fractals, some of which are described in fractal-generating software....

the Mandelbrot set is defined as the set of all c such that J ( f c ) {\displaystyle J(f_{c})} is connected. For parameters outside the Mandelbrot set, the...

probability distribution over the trajectories of points that escape the Mandelbrot fractal. Its name reflects its pareidolic resemblance to classical depictions...

various scales, as illustrated in successive magnifications of the Mandelbrot set. This exhibition of similar patterns at increasingly smaller scales...

in the fractal called the Mandelbrot set was discovered by David Boll in 1991. He examined the behaviour of the Mandelbrot set near the "neck" at (−0.75...

a portmanteau of multiple and Mandelbrot set. The same can be applied to the Julia set, this being called Multijulia set. z ↦ z d + c . {\displaystyle...

R-squared: 0.9478 F-statistic: 91.88 on 1 and 4 DF, p-value: 0.000662 This Mandelbrot set example highlights the use of complex numbers. It models the first 20...

Non-fractal imagery may also be integrated into the artwork. The Julia set and Mandelbrot sets can be considered as icons of fractal art. It was assumed that...

an illustrator and theologian who discovered the Mandelbrot set some 700 years before Benoit Mandelbrot. Udo's works were allegedly discovered by the also-fictional...

point has infinite length. A famous example is the boundary of the Mandelbrot set. Fractal curves and fractal patterns are widespread, in nature, found...

stalks are certain kinds of details to be found empirically in the Mandelbrot set, in the study of fractal geometry. They are so named after the researcher...

tree. A more general notion than self-similarity is self-affinity. The Mandelbrot set is also self-similar around Misiurewicz points. Self-similarity has...

k = 1, …, deg(p). In this way the Newton fractal is similar to the Mandelbrot set, and like other fractals it exhibits an intricate appearance arising...

Paul Nylander using spherical coordinates. A canonical 3-dimensional Mandelbrot set does not exist, since there is no 3-dimensional analogue of the 2-dimensional...

M-set may refer to Sydney Trains M set, a class of electric train Set of uniqueness or Menshov set of harmonic analysis Mandelbrot set, a two-dimensional...

The Mandelbrot Set were an indie/powerpop band from Adelaide, South Australia, who rose to prominence during the "shoegaze" era of the early 1990s. They...

Mandelbrot may refer to: Benoit Mandelbrot (1924–2010), a mathematician associated with fractal geometry Mandelbrot set, a fractal popularized by Benoit...

they pass through a function a set number of times. The best known example of this kind of fractal is the Mandelbrot set, which is based upon the function...

In mathematics, a Misiurewicz point is a parameter value in the Mandelbrot set (the parameter space of complex quadratic maps) and also in real quadratic...

x_{n}=...=x_{1}=x_{0}=f(x_{0})} ). Many chaotic systems such as the Mandelbrot set are emerging from iteration of very simple quadratic non linear functions...

\theta } of the ray that lands: at c in Mandelbrot set on the parameter plane on the critical value:z = c in Julia set on the dynamic plane so : f c = f θ...

is the Julia set for that value of c {\displaystyle c} . This curve is continuous when c {\displaystyle c} is inside the Mandelbrot set; otherwise, it...

finite-parameter families of vector fields on a sphere? MLC conjecture – is the Mandelbrot set locally connected? Many problems concerning an outer billiard, for example...

variable x. Tabulating the bifurcation values again: In the case of the Mandelbrot set for complex quadratic polynomial f ( z ) = z 2 + c {\displaystyle f(z)=z^{2}+c}...

originated in Benoit Mandelbrot's pursuit of a generalized function for a class of shapes known as Julia sets. In 1979, Mandelbrot discovered that one...

dynamics, including a study of the Mandelbrot set. One of their most important results is that the Mandelbrot set is connected. Hubbard graduated with...

An external ray is a curve that runs from infinity toward a Julia or Mandelbrot set. Although this curve is only rarely a half-line (ray) it is called a...

stalks are certain kinds of details that are empirically found in the Mandelbrot set in the study of fractal geometry. In the 1980s, Pickover proposed that...