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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 Mandelbrot set is widely considered the most popular fractal, [44] [45] and has been referenced several times in popular culture. The Jonathan Coulton song "Mandelbrot Set" is a tribute to both the fractal itself and to the man it is named after, Benoit Mandelbrot. [46]
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
By even portioning, Mandelbrot meant that the addends were of same order of magnitude, otherwise he considered the portioning to be concentrated. Given the moment of order q of a random variable, Mandelbrot called the root of degree q of such moment the scale factor (of order q). The seven states are:
Benoit Mandelbrot (1924–2010) – fractal geometry; Katsumi Nomizu (1924–2008) – affine differential geometry; Michael S. Longuet-Higgins (1925–2016) John Leech (1926–1992) Alexander Grothendieck (1928–2014) – algebraic geometry; Branko Grünbaum (1929–2018) – discrete geometry; Michael Atiyah (1929–2019) Lev Semenovich ...
Sierpiński Carpet - Infinite perimeter and zero area Mandelbrot set at islands The Mandelbrot set: its boundary is a fractal curve with Hausdorff dimension 2. (Note that the colored sections of the image are not actually part of the Mandelbrot Set, but rather they are based on how quickly the function that produces it diverges.)
Statistical Self-Similarity and Fractional Dimension", published on 5 May 1967, [12] Mandelbrot discusses self-similar curves that have Hausdorff dimension between 1 and 2. These curves are examples of fractals, although Mandelbrot does not use this term in the paper, as he did not coin it until 1975. The paper is one of Mandelbrot's first ...