9780716711865 / 0716711869

The Fractal Geometry of Nature


Publisher:W. H. Freeman and Company



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About the book:

CONTENTS: I Introduction; II Three Classic Fractals, Tamed; III Galaxies and Eddies; IV Scaling Fractals; V Nonscaling Fractals; VI Self-Mapping Fractals; VII Randomness; VIII Stratified Random Fractals; IX Fractional Brown Fractals; X Random Tremas; Texture; XI Miscellany; XII Of Men and Ideas; List of References; Acknowledgments; Index of Selected Dimensions; Index of Names and Subjects; Update Added in the Second Printing. SYNOPSIS: Clouds are not spheres, mountains are not cones, and lightning does not travel in a straight line. The complexity of nature's shapes differs in kind, not merely degree, from that of the shapes of ordinary geometry. To describe such shapes, Benoit Mandelbrot conceived and developed a new geometry, the geometry of fractal shapes. His work is significant to fields whose diversity is suggested by the following reviews of Fractals: Form, Chance, and Dimension (W. H. Freeman and Company, 1977): "Heartening and illuminating application of advanced mathematics to the beautiful, irregular enigmas of the world." - Marc LeBrun, Co-Evolution Quarterly, Fall, 1977; "A rarity: a picture book of sophisticated contemporary research ideas in mathematics. Here, it concerns recursively defined curves and shapes, whose dimensionality is not a whole number. Amazingly, Mandelbrot shows their relevance to practically every branch of science." - Douglas R. Hofstadter, author of Godel, Escher, Bach; "Written with daring originality . . . I like people who write for glory and not just for money." - I. J. Good, Journal of the American Statistical Association, June 1978. Now that the field has expanded greatly with many active researchers, Mandelbrot presents the definitive overview of the origins of his ideas and their new applications. The Fractal Geometry of Nature is based on his highly acclaimed earlier work, but has much broader and deeper coverage and more extensive illustrations. Whether your interests lie in nature and its shapes, in...

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