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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".
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.
Mandelbrot may refer to: Benoit Mandelbrot (1924–2010), a mathematician associated with fractal geometry Mandelbrot set , a fractal popularized by Benoit Mandelbrot
He was the uncle of Benoit Mandelbrot. Szolem Mandelbrojt (10 January 1899 – 23 September 1983) was a Polish-French mathematician who specialized in mathematical analysis . He was a professor at the Collège de France from 1938 to 1972, where he held the Chair of Analytical Mechanics and Celestial Mechanics.
In probability theory and statistics, the Zipf–Mandelbrot law is a discrete probability distribution.Also known as the Pareto–Zipf law, it is a power-law distribution on ranked data, named after the linguist George Kingsley Zipf, who suggested a simpler distribution called Zipf's law, and the mathematician Benoit Mandelbrot, who subsequently generalized it.
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.
Chaos: Making a New Science was the first popular book about chaos theory. It describes the Mandelbrot set, Julia sets, and Lorenz attractors without using complicated mathematics.
A generalization of Zipf's law is the Zipf–Mandelbrot law, proposed by Benoit Mandelbrot, whose frequencies are: (;,,) = (+) . [clarification needed] The constant C is the Hurwitz zeta function evaluated at s.