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Benoit B. Mandelbrot [a] [b] (20 November 1924 – 14 October 2010) was a Polish-born French-American mathematician and polymath with broad interests in the practical sciences, especially regarding what he labeled as "the art of roughness" of physical phenomena and "the uncontrolled element in life".
Mandelbrot (Yiddish: מאַנדלברויט), [1] [2] [3] with a number of variant spellings, [A] and called mandel bread or kamish in English-speaking countries and kamishbrot in Ukraine, is a type of cookie found in Ashkenazi Jewish cuisine and popular amongst Eastern European Jews.
Mandelbrot may refer to: Benoit Mandelbrot (1924–2010), a mathematician associated with fractal geometry Mandelbrot set , a fractal popularized by Benoit Mandelbrot
A mosaic made by matching Julia sets to their values of c on the complex plane. The Mandelbrot set is a map of connected Julia sets. As a consequence of the definition of the Mandelbrot set, there is a close correspondence between the geometry of the Mandelbrot set at a given point and the structure of the corresponding Julia set. For instance ...
According to Benoit Mandelbrot, "A fractal is by definition a set for which the Hausdorff-Besicovitch dimension strictly exceeds the topological dimension." [1] Presented here is a list of fractals, ordered by increasing Hausdorff dimension, to illustrate what it means for a fractal to have a low or a high dimension.
Also, the Mandelbrot set and various other fractals are covered by a finite area, but have an infinite perimeter (in fact, there are no two distinct points on the boundary of the Mandelbrot set that can be reached from one another by moving a finite distance along that boundary, which also implies that in a sense you go no further if you walk ...
The Fractal Geometry of Nature is a revised and enlarged version of his 1977 book entitled Fractals: Form, Chance and Dimension, which in turn was a revised, enlarged, and translated version of his 1975 French book, Les Objets Fractals: Forme, Hasard et Dimension.
Because the Mandelbrot set is full, [12] any point enclosed by a closed shape whose borders lie entirely within the Mandelbrot set must itself be in the Mandelbrot set. Border tracing works by following the lemniscates of the various iteration levels (colored bands) all around the set, and then filling the entire band at once.