Search results
Results from the WOW.Com Content Network
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".
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.
A recursive acronym is an acronym that refers to itself, and appears most frequently in computer programming.The term was first used in print in 1979 in Douglas Hofstadter's book Gödel, Escher, Bach: An Eternal Golden Braid, in which Hofstadter invents the acronym GOD, meaning "GOD Over Djinn", to help explain infinite series, and describes it as a recursive acronym. [1]
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.
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:
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.
AOL latest headlines, entertainment, sports, articles for business, health and world news.
The usage of the word "gasket" to refer to the Sierpiński triangle refers to gaskets such as are found in motors, and which sometimes feature a series of holes of decreasing size, similar to the fractal; this usage was coined by Benoit Mandelbrot, who thought the fractal looked similar to "the part that prevents leaks in motors". [23]