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....

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

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...

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

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...

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...

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...

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

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

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...

the tricorn, sometimes called the Mandelbar set, is a fractal defined in a similar way to the Mandelbrot set, but using the mapping z ↦ z ¯ 2 + c {\displaystyle...

\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...

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...

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...

{\displaystyle c} is near the center of one of the period three bulbs of the Mandelbrot set for a complex quadratic map. It is named after French mathematician...

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...

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

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...

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...

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...

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...

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

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}...

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

cardioid of the Mandelbrot set, in which case it is in the interior of a filled-in Julia set, and therefore belongs to the Fatou set (strictly to the...

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...