Fractals: Form, Chance, and Dimension

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Echo Point Books and Media, Feb 25, 2020 - Mathematics - 384 pages

Discover the Hidden Mathematics of Modern Geometry

Fractals, the never-ending geometric-mathematical patterns existing throughout nature, are revealed in the shapes of continents, galaxies, snowflakes, and grains of sand. In this fascinating and seminal volume, renowned pioneering-mathematician Benoit B. Mandelbrot explains his work on fractal geometry, mathematically translating the description of these complex shapes of nature.

Until Mandelbrot developed the concept of fractal geometry in the 1960s and 70s, most mathematicians believed these irregular shapes were too fragmented and amorphous to be described mathematically. Mandelbrot's revolutionary concept brought order to a variety of seemingly unsolvable problems in physics, biology, and financial markets.

Broad in application, this groundbreaking work will inform not just mathematicians, but anyone that appreciates the natural elegance of patterns made manifest. Featuring illustrations of mathematically defined shapes, Mandelbrot describes how geometric patterns relate to every aspect of the physical world around us.

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About the author (2020)

Benoit Mandelbrot was a graduate of Ecole Polytechnique and the University of Paris, and received a masters degree in aeronautics at the California Institute of Technology. In 1958 he joined the IBM Thomas J. Research Council, where he was an IBM Fellow, taking periodic leaves to teach at Harvard University as Visiting Professor of Economics, and, later, of applied mathematics. He also taught at Yale, the University of Paris-Sud, M.I.T., and the Albert Einstein College of Medicine. He was a Fellow of the Guggenheim Foundation, Trumbull Lecturer at Yale, Samuel Wilks Lecturer at Princeton, and Abraham Wald Lecturer at Columbia. It was as Lecturer at Collège de France that he gave in 1973 and 1974 the lessons which eventually were developed into the present essay; he discovered the Mandelbrot set in 1980 through his use of the computing power available to him at IBM.

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