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The Fractal Geometry of Nature
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› Besuchen Sie die Seite von Benoit Mandelbrot auf Amazon
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Imagine an equilateral triangle. Now, imagine smaller equilateral triangles perched in the center of each side of the original triangle--you have a Star of David. Now, place still smaller equilateral triangles in the center of each of the star's 12 sides. Repeat this process infinitely and you have a Koch snowflake, a mind-bending geometric figure with an infinitely large perimeter, yet with a finite area. This is an example of the kind of mathematical puzzles that this book addresses.
The Fractal Geometry of Nature is a mathematics text. But buried in the deltas and lambdas and integrals, even a layperson can pick out and appreciate Mandelbrot's point: that somewhere in mathematics, there is an explanation for nature. It is not a coincidence that fractal math is so good at generating images of cliffs and shorelines and capillary beds.
Pressestimmen
"A rarity: a picture book of sophisticated contemporary research ideas in mathematics."--Douglas Hofstadter, author of "Godel, Escher, Bach"
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This tome is the immortal classic that introduces fractals to the layman and scholar alike. The mechanics and beauty of fractals are presented in a very readable manner that is sure to pique the interest of anyone seeking a deterministic, yet almost supernaturally pervasive paradigm of the structure of the universe. This book fundamentally affected my personal outlook on nature irrecovably. I would advise leaving it on the coffee table for your children to examine.
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Mandelbrot's update of his classic work is certainly eye-catching. However, just like its forerunner, it fails to answer the simplest questions, including, "How do I calculate the fractal dimension of this curve?" and "How can I manage to plot the Julia set for myself?" The answers to such questions have to be gleaned by the intelligent--and mathematically sophisticated--reader for himself. (One sees this phenomenon all the time in "advanced" mathematics books. It means that either [a] the author has his head stuck in the clouds and expects the reader to use divination, or [b] he prefers to keep his readers ignorant.) For a much more practical and rewarding discussion, read "The Science of Fractal Images" edited by Peitgen and Saupe. The math is clear; the algorithms are plainly stated for the PC enthusiast with some simple programming skills; and the color plates are astounding.
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A set for which the Hausdorff Besicovitch dimension strictly exceeds the topological dimension.
The definition of a fractal pretty much sets the tone for the book. There are mostly definitions and monochrome diagrams to explain the more classical fractals. The book does shows some practical geometric uses for fractals but I would not let it get anywhere near my Koch Curve.
I am not being kind to this book as there is a color section in the center. That shows "The Great Wave" by Katsushika Hokusai (1760-12849.) And an extensive reference section.
The book its self could easily be used as a text book for school.
Fractals: Hunting the Hidden DA set for which the Hausdorff Besicovitch dimension strictly exceeds the topological dimension.
The definition of a fractal pretty much sets the tone for the book. There are mostly definitions and monochrome diagrams to explain the more classical fractals. The book does shows some practical geometric uses for fractals but I would not let it get anywhere near my Koch Curve.
I am not being kind to this book as there is a color section in the center. That shows "The Great Wave" by Katsushika Hokusai (1760-12849.) And an extensive reference section.
The book its self could easily be used as a text book for school.
Fractals: Hunting the Hidden Dimension [Blu-ray]~ USA
[[ASIN:0201554402 An Eye For Fractals: A Graphic And Photographic Essay (Studies in Nonlinearity)
The definition of a fractal pretty much sets the tone for the book. There are mostly definitions and monochrome diagrams to explain the more classical fractals. The book does shows some practical geometric uses for fractals but I would not let it get anywhere near my Koch Curve.
I am not being kind to this book as there is a color section in the center. That shows "The Great Wave" by Katsushika Hokusai (1760-12849.) And an extensive reference section.
The book its self could easily be used as a text book for school.
Fractals: Hunting the Hidden DA set for which the Hausdorff Besicovitch dimension strictly exceeds the topological dimension.
The definition of a fractal pretty much sets the tone for the book. There are mostly definitions and monochrome diagrams to explain the more classical fractals. The book does shows some practical geometric uses for fractals but I would not let it get anywhere near my Koch Curve.
I am not being kind to this book as there is a color section in the center. That shows "The Great Wave" by Katsushika Hokusai (1760-12849.) And an extensive reference section.
The book its self could easily be used as a text book for school.
Fractals: Hunting the Hidden Dimension [Blu-ray]~ USA
[[ASIN:0201554402 An Eye For Fractals: A Graphic And Photographic Essay (Studies in Nonlinearity)
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Good, one of the first, but not the best
The book is still a milestone in the history of fractals, but it gets currently lost among the many available publications. Lesen Sie weiter...
Veröffentlicht am 22. Juni 2000 von Massimiliano Celaschi
This book started it all
This book is by far the very root by which chaos and the interrelations with that of nature came into existance. Lesen Sie weiter...
Am 15. Juni 1998 veröffentlicht
The Start of the Fractal Era of Mankind
One can not praise a masterwork enough. If you have the money buy it. Your unique Associates ID is: thefractaltransl.
Am 19. März 1998 veröffentlicht
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