MANDELBROT, BENOIT B. / الرياضيات / الباحثون

المركز الدولي للبحث العلمي




Sterling Professor of Mathematical Sciences, Mathematics Department, Yale University
New Haven, USA

IBM Fellow Emeritus, TJ Watson Research Center, International Business
Machines Corporation

مواضيع البحث

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

Nature is filled with complex geometrical shapes such as seashore lines, branching patterns of rivers, biological shapes, and even the curves of currency exchange rates. There is a common feature in such complex shapes: their self-similarity. This is the property that, when a part of a shape is enlarged, the same type of structure appears again. Dr. Mandelbrot discovered that self-similarity is the universal property that underlies such complex shapes, and he coined the expression "fractal." Furthermore, he has illustrated its properties mathematically and founded a new methodology for analyzing complex systems.


1985 Barnard Medal for Meritorious Service to Science "Magna est Veritas:"
1986 Franklin Medal for Signal and Eminent Service in Science
1988 Charles Proteus Steinmetz Medal
1988 Alumni Distinguished Service Award for Outstanding Achievement; Caltech
1988 Senior Award (Humboldt Preis)
1988 "Science for Art" Prize
1989 Harvey Prize for Science and Technology
1991 Nevada Prize
1993 Wolf Foundation Prize for Physics
1994 Honda Prize
1996 Médaille de Vermeil: de la ville de Paris
1999 John Scott Award
1999 Lewis Fry Richardson Medal
2002 William Procter Prize for Scientific Achievement: Sigma Xi
2003 Japan Prize

Member (honorary), Societe Physique de France.
Fellow, American Physical Society.
Fellow, American Association for the Advancement of Science.
Member, American Mathematical Society.


B.B.Mandelbrot, The Fractal Geometry of Nature, W.H.Freeman and Company@(NewYork),1982.

B.B.Mandelbrot, Fractals and Scaling in Finance: Discontinuity, Concentration, Risk, New York: Springer, 1997.

B.B.Mandelbrot, Multifractals and 1/f Noise : Wild Self-Affinity in Physics, New York: Springer, 1999.

B.B.Mandelbrot, Gaussian Self-Affinity & Fractals: Globality, the Earth, 1/f, & R/S, New York: Springer, 2002.

M. L. Frame & B.B.Mandelbrot, Fractals, Graphics and Mathematical Education, Washington DC: Mathematical Association of America & Cambridge UK: The University Press, 2002.

B.B.Mandelbrot, The variation of certain speculative prices. The Journal of Business of the University of Chicago: 36, 394-419. 1963.

B.B.Mandelbrot, Random walks, fire damage amount, and other Paretian risk phenomena,Operations Research 12, 582-585, 1964.

B.B.Mandelbrot, How long is the coast of Britain? Statistical self-similarity and fractional dimension, Science 155, 636-638, 1967.

B.B.Mandelbrot, Some noises with 1/f spectrum, a bridge between direct current and white noise, IEEE Transactions on Information Theory 13, 289-298, 1967.

B.B.Mandelbrot, A population birth and mutation process, I: Explicit distribution for the number of mutants in an old culture of bacteria, Journal of Applied Probability 11, 437-444, 1974.

B.B.Mandelbrot, Intermittent turbulence in self-similar cascades; divergence of high moments and dimension of carrier, Journal of Fluid Mechanics, 62, 331-358, 1974.

B.B.Mandelbrot, Stochastic models for the Earth's relief, the shape and the fractal dimension of the coastlines, and the number-area rule of islands, Proceedings of the National Academy of Sciences (USA) 72, 3825-3828, 1975.

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