The Fractal Geometry Of Nature

Author: Benoit B. Mandelbrot
Publisher: Macmillan
ISBN: 9780716711865
Size: 60.77 MB
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Three classic fractals, tamed. Galaxies and eddies. Scaling fractals. Nonscaling fractals. Self-mapping fractals. Randomness. Stratified random fractals. Fractional brown fractals. A book-within-the-book, in color. Random tremas; texture. Miscellany. Of men and ideas.

Is God A Mathematician

Author: Mario Livio
Publisher: Simon and Schuster
ISBN: 9781416594437
Size: 16.25 MB
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Bestselling author and astrophysicist Mario Livio examines the lives and theories of history’s greatest mathematicians to ask how—if mathematics is an abstract construction of the human mind—it can so perfectly explain the physical world. Nobel Laureate Eugene Wigner once wondered about “the unreasonable effectiveness of mathematics” in the formulation of the laws of nature. Is God a Mathematician? investigates why mathematics is as powerful as it is. From ancient times to the present, scientists and philosophers have marveled at how such a seemingly abstract discipline could so perfectly explain the natural world. More than that—mathematics has often made predictions, for example, about subatomic particles or cosmic phenomena that were unknown at the time, but later were proven to be true. Is mathematics ultimately invented or discovered? If, as Einstein insisted, mathematics is “a product of human thought that is independent of experience,” how can it so accurately describe and even predict the world around us? Physicist and author Mario Livio brilliantly explores mathematical ideas from Pythagoras to the present day as he shows us how intriguing questions and ingenious answers have led to ever deeper insights into our world. This fascinating book will interest anyone curious about the human mind, the scientific world, and the relationship between them.

Fractals A Very Short Introduction

Author: K. J. Falconer
Publisher: Oxford University Press
ISBN: 0199675988
Size: 59.80 MB
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An essential discussion of the popular science and mathematics behind fractals reveals how fractal shapes can be found everywhere in nature from clouds to coastlines, explaining how basic concepts in fractal geometry produced a revolution in mathematical understandings of patterns in the 20th century. Original.

Measure Topology And Fractal Geometry

Author: Gerald Edgar
Publisher: Springer Science & Business Media
ISBN: 0387747494
Size: 53.37 MB
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Based on a course given to talented high-school students at Ohio University in 1988, this book is essentially an advanced undergraduate textbook about the mathematics of fractal geometry. It nicely bridges the gap between traditional books on topology/analysis and more specialized treatises on fractal geometry. The book treats such topics as metric spaces, measure theory, dimension theory, and even some algebraic topology. It takes into account developments in the subject matter since 1990. Sections are clear and focused. The book contains plenty of examples, exercises, and good illustrations of fractals, including 16 color plates.

The Mis Behaviour Of Markets

Author: Benoit B. Mandelbrot
Publisher: Profile Books
ISBN: 1847651550
Size: 64.65 MB
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This international bestseller, which foreshadowed a market crash, explains why it could happen again if we don't act now. Fractal geometry is the mathematics of roughness: how to reduce the outline of a jagged leaf or static in a computer connection to a few simple mathematical properties. With his fractal tools, Mandelbrot has got to the bottom of how financial markets really work. He finds they have a shifting sense of time and wild behaviour that makes them volatile, dangerous - and beautiful. In his models, the complex gyrations of the FTSE 100 and exchange rates can be reduced to straightforward formulae that yield a much more accurate description of the risks involved.

Fractals And Scaling In Finance

Author: Benoit B. Mandelbrot
Publisher: Springer Science & Business Media
ISBN: 1475727631
Size: 65.77 MB
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Mandelbrot is world famous for his creation of the new mathematics of fractal geometry. Yet few people know that his original field of applied research was in econometrics and financial models, applying ideas of scaling and self-similarity to arrays of data generated by financial analyses. This book brings together his original papers as well as many original chapters specifically written for this book.

Fractal Geometry In Architecture And Design

Author: Carl Bovill
Publisher: Springer Science & Business Media
ISBN: 1461208432
Size: 41.77 MB
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na broad sense Design Science is the grammar of a language of images Irather than of words. Modern communication techniques enable us to transmit and reconstitute images without needing to know a specific verbal sequence language such as the Morse code or Hungarian. International traffic signs use international image symbols which are not specific to any particular verbal language. An image language differs from a verbal one in that the latter uses a linear string of symbols, whereas the former is multi dimensional. Architectural renderings commonly show projections onto three mutual ly perpendicular planes, or consist of cross sections at different altitudes capa ble of being stacked and representing different floor plans. Such renderings make it difficult to imagine buildings comprising ramps and other features which disguise the separation between floors, and consequently limit the cre ative process of the architect. Analogously, we tend to analyze natural struc tures as if nature had used similar stacked renderings, rather than, for instance, a system of packed spheres, with the result that we fail to perceive the system of organization determining the form of such structures. Perception is a complex process. Our senses record; they are analogous to audio or video devices. We cannot, however, claim that such devices perceive.

Fractals In Biology And Medicine

Author: Gabriele A. Losa
Publisher: Springer Science & Business Media
ISBN: 9783764364748
Size: 10.66 MB
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In March 2000 leading scientists gathered at the Centro Seminariale Monte Verità, Ascona, Switzerland, for the Third International Symposium on "Fractals 2000 in Biology and Medicine". This interdisciplinary conference was held over a four-day period and provided stimulating contributions from the very topical field Fractals in Biology and Medicine. This Volume III in the MBI series highlights the growing power and efficacy of the fractal geometry in understanding how to analyze living phenomena and complex shapes. Many biological objects, previously considered as hopelessly far from any quantitative description, are now being investigated by means of fractal methods. Researchers currently used fractals both as theoretical tools, to shed light on living systems` self-organization and evolution, and as useful techniques, capable of quantitatively analyzing physiological and pathological cell states, shapes and ultrastructures. The book should be of interest to researchers and students from Molecular and C