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# Topic: Benoit Mandelbrot

###### In the News (Sun 16 Jun 19)

 Benoit Mandelbrot   (Site not responding. Last check: 2007-10-16) Mandelbrot was born into a family with a very academic tradition. Mandelbrot's family emigrated from Poland to France in 1936 and one of his uncles took responsibility for his education. Mandelbrot returned to France briefly, but in 1958 he returned permanently, and began his long standing and most fruitful collaboration with IBM as a Research Fellow and Research Professor. www.stetson.edu /~efriedma/periodictable/html/Mt.html   (444 words)

 Benoît Mandelbrot - Wikipedia, the free encyclopedia Benoît B. Mandelbrot (born November 20, 1924) is a Polish-born French mathematician and leading proponent of fractal geometry. Mandelbrot brought these objects together for the first time and highlighted their common properties, such as self-similarity (sometimes partial or statistical), scale invariance and (usually) non-integer Hausdorff dimension. Mandelbrot's informal and passionate style of writing and his emphasis on visual and geometric intuition (supported by the inclusion of numerous illustrations) made The Fractal Geometry of Nature accessible to non-specialists. en.wikipedia.org /wiki/Beno%C3%AEt_Mandelbrot   (909 words)

 [No title]   (Site not responding. Last check: 2007-10-16) Benoit B. Mandelbrot (born November 20, 1924) is a French mathematician, largely responsible for the present interest in fractal geometry. Mandelbrot was born into a family with a strong academic tradition - his mother was a doctor and his uncle, Szolem Mandelbrot, was a famous Parisian mathematician. Mandelbrot originated what is now known as fractal geometry and the fractal called the Mandelbrot set is named after him. www.informationgenius.com /encyclopedia/b/be/benoit_mandelbrot.html   (194 words)

 Explore: Mandelbrot Set The Mandelbrot set was introduced in 1980, showing how complex phenomena could be generated from simple rules iterated repeatedly. Benoit Mandelbrot, often referred to as the father of fractals, almost single-handedly created a new geometry of nature. He introduced the concept of fractal dimension by suggesting that the dimension of a coastline, for example, must fall somewhere between the dimensions of a smooth curve (with dimension one) and a smooth surface (with dimension two). library.wolfram.com /explorations/explorer/Mandelbrot.html   (220 words)

 Benoit Mandelbrot   (Site not responding. Last check: 2007-10-16) Mandelbrot received his diploma from L'École Polytechnique, Paris, in 1947, his Master of Science in Aeronautics from the California Institute of Technology in 1948, and his Ph.D. in Mathematical Sciences from the University of Paris in 1952. In the mid-1970s Mandelbrot coined the word "fractal" (from the Latin word "fractus", meaning fractured, broken) to label objects, shapes or behaviors that have similar properties (self-similarity) at all levels of magnification or across all times, and which dimension, being greater than one but smaller than two, cannot be expressed as an integer. Mandelbrot's own work is a case of multidisciplinarity: his doctoral thesis (a mathematical analysis of the distribution of words in the English language, U. de Paris, 1952) combined linguistics with the tools of statistical thermodynamics. www.fractovia.org /people/mandelbrot.html   (851 words)

 Fractal Geometry His uncle, Szolem Mandelbrot, was a member of an elite group of French mathematicians in Paris known as the "Bourbaki." Benoit Mandelbrot was born in Warsaw in 1924 to a Lithuanian Jewish family. But Mandelbrot conceived and developed a new fractal geometry of nature based on the fourth dimension and Complex numbers which is capable of describing mathematically the most amorphous and chaotic forms of the real world. Mandelbrot discovered that the fourth dimension of fractal forms includes an infinite set of fractional dimensions which lie between the zero and first dimension, the first and second dimension and the second and third dimension. www.fractalwisdom.com /FractalWisdom/fractal.html   (2550 words)

 IBM Research | Press Resources | Benoit Mandelbrot to receive prestigious Japan Prize Mandelbrot's multi-disciplinary explorations began fifty years ago, when his doctoral thesis in 1952 combined linguistics (the frequency distribution of words) with the tools of statistical thermodynamics. Mandelbrot has also found self-similarity to hold true in the field of water resources, and his study of floods and droughts in the Nile River Basin revealed and modeled the persistence of weather and the tendency of droughts or floods to come in clusters. Mandelbrot re-introduced the eye to the study of mathematics where his contributions have been twofold. domino.research.ibm.com /comm/pr.nsf/pages/news.20021218_Benoit_Mandelbrot.html   (646 words)

 Benoit Mandelbrot, Fractals and Astronomy (Part 1) Mandelbrot discovered that complex phenomenon in a variety of sciences, including astronomy, could be understood in terms of fractals. After obtaining his Ph.D., Mandelbrot conducted a wide variety of investigations that went, as he described it, “in a number of directions.” He began to realize there was an underlying theme to what he had been working on: these “useless” mathematical objects discovered earlier had a use. Mandelbrot realized that the most useful of these was the Hausdorff dimension (though it is the hardest to calculate). www.umich.edu /~lowbrows/reflections/1998/dsnyder.3.html   (1262 words)

 Biography of Benoit Mandelbrot   (Site not responding. Last check: 2007-10-16) Benoit Mandelbrot was born in Warsaw, Poland, in 1924. Mandelbrot, after moving with his family to France in 1936, attended the Lycée Rolin and the Ecole Polytechnique (a pair of French colleges), as well as Caltech and Princeton, which he was recommended to by John von Neumann. Mandelbrot is responsible for most of the creation of fractal geometry and chaos theory; two concepts that threaten to change the way mathematics is viewed in the world today. www.andrews.edu /~calkins/math/biograph/biomandl.htm   (595 words)

 Edge: A THEORY OF ROUGHNESS: A Talk with Benoit Mandelbrot Mandelbrot is best known as the founder of fractal geometry which impacts mathematics, diverse sciences, and arts, and is best appreciated as being the first broad attempt to investigate quantitatively the ubiquitous notion of roughness. BENOIT MANDELBROT is Sterling Professor of Mathematical Sciences at Yale University and IBM Fellow Emeritus (Physics) at the IBM T.J. Watson Research Center. It may not be widely appreciated that the discovery of that set had consisted in empowering the eye again, in inspecting pictures beyond counting and on their basis stating a number of observations and conjectures to which I drew the mathematicians' attention. www.edge.org /3rd_culture/mandelbrot04/mandelbrot04_index.html   (3801 words)

 Benoit mandelbrot, - Digital Artform: Benoit Mandelbrot Mandelbrot was the first person to use a computer to graphically represent the complex number plane. Benoit Mandelbrot is not an artist in the usual sense of the word. Benoit Mandelbrot was born in Warsaw, Poland, in 1924. directorytool.com /deot/benoit-mandelbrot.htm   (275 words)

 M2 Presswire: Yale mathematician Benoit Mandelbrot elected to the American Philosophical Society.@ HighBeam Research   (Site not responding. Last check: 2007-10-16) Yale mathematician Benoit Mandelbrot elected to the American Philosophical Society. New Haven, Conn. -- Benoit B. Mandelbrot, Sterling Professor of Mathematical Sciences at Yale University, was inducted to membership in the American Philosophical Society, the oldest learned society in the United States, founded in 1743 by Benjamin Franklin for the purpose of "promoting useful knowledge." Mandelbrot, best known as the "Father of Fractals" is a member of the National Academy of... www.highbeam.com /library/doc0.asp?DOCID=1G1:117866617&refid=ip_encyclopedia_hf   (179 words)

 Alibris: Benoit Mandelbrot Mandelbrot is a world-renowned scientist, known for his pioneering research in fractal geometry. In this book Mandelbrot brings together new material and his original research in applying ideas of discontinuity, scaling, and self-similarity to the analysis of econometric and financial models, and for evaluating risks in trading strategies. In this volume, a world renowned scientist, Benoit Mandelbrot, defends the view that multifractals are intimately interrelated through the two fractal themes of "wildness" and "self-affinity". www.alibris.com /search/books/author/Benoit_Mandelbrot   (611 words)

 Benoît Mandelbrot - Wikipedia, the free encyclopedia   (Site not responding. Last check: 2007-10-16) He is Sterling Professor of Mathematical Sciences, Emeritus at Yale University and IBM at the Thomas J. Watson Research Center. Building on previous work by Julia and by Pierre Fatou, Mandelbrot used a computer to plot images of the Julia sets of the equation z While investigating how the topology of these Julia sets depended on the complex parameter c, he discovered the Mandelbrot set fractal that is now named after him. www.kernersville.us /project/wikipedia/index.php/Benoit_Mandelbrot   (887 words)

 FOA: 3.2.1.2 Benoit Mandelbrot's explanation   (Site not responding. Last check: 2007-10-16) Mandelbrot's background as a physicist is clear when he considers the message decoder as a physical piece of apparatus, ... Mandelbrot proposed a more general form of Zipf's Law: F(r)={C\over{(r+b)^\alpha}} that has proved important to analysis of the relationship between word frequencies and their rank (cf. Mandelbrot also suggested how this model might be applied within a model of cognition: Whatever the detailed structure of the brain it recodes information many times. www.cs.ucsd.edu /~rik/foa/l2h/foa-3-2-1-2.html   (511 words)

 The (Mis)Behaviour of Markets: A Fractal View of Risk, Ruin and Reward by Benoit Mandelbrot and Richard Hudson   (Site not responding. Last check: 2007-10-16) Benoit B. Mandelbrot, one of the century's most influential mathematicians, is world-famous for making mathematical sense of a fact everybody knows but that geometers from Euclid on down had never assimilated: Clouds are not round, mountains are not cones, coastlines are not smooth. In his first book for a general audience, Mandelbrot, with co-author Richard L. Hudson, shows how the dominant way of thinking about the behaviour of markets--a set of mathematical assumptions a century old and still learned by every MBA and financier in the world--simply does not work. With his fractal tools, Mandelbrot has gotten to the bottom of how financial markets really work, and in doing so, he describes the volatile, dangerous (and strangely beautiful) properties that financial experts have never before accounted for. www.marketsandfractalsbook.com   (391 words)

 Mandelbrot - Wikipedia, the free encyclopedia Benoît Mandelbrot, a French mathematician largely responsible for later interest in fractal geometry Mandelbrot set, a fractal popularized by Benoît Mandelbrot This is a disambiguation page, a list of pages that otherwise might share the same title. en.wikipedia.org /wiki/Mandelbrot   (97 words)

 Powell's Books - The (Mis)Behavior of Markets: A Fractal View of Risk, Ruin, and Reward by Benoit Mandelbrot Benoit B. Mandelbrot, one of the century's most influential mathematicians, is world-famous for making mathematical sense of a fact everybody knows but that geometers from Euclid on down had never assimilated: Clouds are not round, mountains are not cones, coastlines are not smooth. In his first book for a general audience, Mandelbrot, with co-author Hudson, shows how the dominant way of thinking about the behavior of markets — a set of mathematical assumptions a century old and still learned by every MBA and financier in the world — simply does not work. Benoit Mandelbrot is Sterling Professor of Mathematical Sciences at Yale University and a Fellow Emeritus at IBM's Thomas J. Watson Laboratory. www.powells.com /biblio?show=0465043550   (716 words)

 Digital Artform: Benoit Mandelbrot I saw on boingboing that Benoit Mandelbrot, who coined the term fractal geometry, turns eighty next week. I was lucky enough to be part of the group at R/Greenberg Associates in New York that helped bring one of Mandelbrot's and Dr. Richard Voss's famous fractal terrains to popular attention by animating a fly-through of it in a 1987 IBM television commercial. The ideas are Benoit Mandelbrots, and the implementation was Richard Voss's. www.digitalartform.com /archives/2004/11/benoit_mandelbr.html   (214 words)

 The (Mis)behavior of Markets Benoit Mandelbrot has had a remarkable career which includes seminal work in theoretical and applied mathematics. Mandelbrot might be largely unknown to the wider world, but for the beautiful pictures that can be produced on a computer using the fractal equations he popularized (including the famous Mandelbrot set, named after it's discoverer). Benoit Mandelbrot is a great mathematician, but he is not a practitioner in finance. www.bearcave.com /bookrev/misbehavior_of_markets.html   (2163 words)

 The Mandelbrot Set The outline of the Mandelbrot set is produced by a trick called the escape time algorithm. You may have noticed that the central feature of the Mandelbrot set is basically a series of disks. The whole Mandelbrot set is contained in the complex plane such that a circle of radius 2.5 centered at zero would completely enclose it. www.mcasco.com /mset.html   (1692 words)

 Sigma Xi: The Scientific Research Society: Benoit Mandelbrot   (Site not responding. Last check: 2007-10-16) Pioneering mathematician Benoit B. Mandelbrot, known as the creator of fractal geometry, is one of the few living mathematicians whose originality has given birth to entire disciplines. In 1958, Mandelbrot moved to the United States and joined IBM, delving into processes with unusual statistical properties and geometric features. Mandelbrot joined Yale University in 1987 and is now Sterling Professor of Mathematical Sciences. www.sigmaxi.org /programs/prizes/procter.mandelbrot.shtml   (250 words)

 Ecole Polytechnique - Benoît Mandelbrot's interview Class of 1944, Benoît Mandelbrot is highly regarded in the international scientific spheres for his work on fractal theory. Mandelbrot, however, has never wanted to draw lines between disciplines: for him, a math equation could end up putting financing principles as well as physics to good use. A Professor at Yale University, honorary member of the French Society of Physics, and member of the National Academy of Sciences, Benoît Mandelbrot is highly regarded in the international scientific spheres for his work on fractal theory. www.polytechnique.edu /interview.php?id=12   (777 words)

 Benoit - Mandelbrot Set   (Site not responding. Last check: 2007-10-16) Benoit is a Mandelbrot set rendering program implemented in the Java programming language. Well, I am fascinated by the Mandelbrot set and was also interested in implementing the program using arbitrary numeric precision. Benoit requires the Java 2 Platform, Standard Edition version 1.4 or higher. www.bluemarsh.com /java/benoit   (139 words)

 Benoit B. Mandelbrot Biography / Biography of Benoit B. Mandelbrot Main Biography The Polish-born French-American mathematician Benoit B. Mandelbrot (born 1924) is the inventor of fractals. Benoit Mandelbrot was born in Warsaw, Poland, on November 20, 1924. Each Biography is written by a biographical expert or professional educator and is a complete resource on the individual. www.bookrags.com /biography-benoit-b-mandelbrot   (242 words)

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