Benoit Mandelbrot


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Benoit Mandelbrot

From Wikipedia, the free encyclopedia (20120518)

Benoît B. Mandelbrot (20 November 1924 – 14 October 2010) was a French American mathematician. Born in Poland, he moved to France with his family when he was a child. Mandelbrot spent much of his life living and working in the United States, and he acquired dual French and American citizenship.

Mandelbrot worked on a wide range of mathematical problems, including mathematical physics and quantitative finance, but is best known as the father of fractal geometry. He coined the term fractal and described the Mandelbrot set. Mandelbrot also wrote books and gave lectures aimed at the general public.


Research career

From 1951 onward, Mandelbrot worked on problems and published papers not only in mathematics but in applied fields such as information theory, economics, and fluid dynamics. He became convinced that two key themes, fat tails and self-similar structure, ran through a situation of problems encountered in those fields.

Mandelbrot found that price changes in financial markets did not follow a Gaussian distribution, but rather Lévy stable distributions having theoretically infinite variance. He found, for example, that cotton prices followed a Lévy stable distribution with parameter α equal to 1.7 rather than 2 as in a Gaussian distribution. "Stable" distributions have the property that the sum of many instances of a random variable follows the same distribution but with a larger scale parameter.[12]

Mandelbrot also put his ideas to work in cosmology. He offered in 1974 a new explanation of Olbers' paradox (the "dark night sky" riddle), demonstrating the consequences of fractal theory as a sufficient, but not necessary, resolution of the paradox. He postulated that if the stars in the universe were fractally distributed (for example, like Cantor dust), it would not be necessary to rely on the Big Bang theory to explain the paradox. His model would not rule out a Big Bang, but would allow for a dark sky even if the Big Bang had not occurred.[13]

In 1975, Mandelbrot coined the term fractal to describe these structures, and published his ideas in Les objets fractals, forme, hasard et dimension (1975; an English translation Fractals: Form, Chance and Dimension was published in 1977).[14] Mandelbrot developed here ideas from the article Deux types fondamentaux de distribution statistique[15] (1938; an English translation Two Basic Types of Statistical Distribution) of Czech geographer, demographer and statistician Jaromír Korčák.


In 1982, Mandelbrot expanded and updated his ideas in The Fractal Geometry of Nature.[16] This influential work brought fractals into the mainstream of professional and popular mathematics, as well as silencing critics, who had dismissed fractals as "program artifacts".

Mandelbrot left IBM in 1987, after 35 years and 12 days, when IBM decided to end pure research in his division



Benoît Mandelbrot

De Wikipedia, la enciclopedia libre (20120518)

Benoît Mandelbrot (Varsovia, Polonia, 20 de noviembre de 1924Cambridge, Estados Unidos, 14 de octubre de 2010[1] ) fue un matemático conocido por sus trabajos sobre los fractales. Es considerado el principal responsable del auge de este dominio de las matemáticas


En 1967 publicó en Science «¿Cuánto mide la costa de Gran Bretaña?», donde se exponen sus ideas tempranas sobre los fractales.


Logros científicos

Fue el principal creador de la Geometría Fractal, al referirse al impacto de esta disciplina en la concepción e interpretación de los objetos que se encuentran en la naturaleza. En 1982 publicó su libro Fractal Geometry of Nature, en el que explicaba sus investigaciones en este campo. La geometría fractal se distingue por una aproximación más abstracta a la dimensión de la que caracteriza a la geometría convencional.

El profesor Mandelbrot se interesó por cuestiones que nunca antes habían preocupado a los científicos, como los patrones por los que se rigen la rugosidad o las grietas y fracturas en la naturaleza.

Mandelbrot sostuvo que los fractales, en muchos aspectos, son más naturales, y por tanto mejor comprendidos intuitivamente por el hombre, que los objetos basados en la geometría euclidiana, que han sido suavizados artificialmente.

Las nubes no son esferas, las montañas no son conos, las costas no son círculos, y las cortezas de los árboles no son lisas, ni los relámpagos viajan en una línea recta.

Mandelbrot, de su libro Introduction to The Fractal Geometry of Nature