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Author: C.A. Pickover
Publisher: Elsevier
ISBN: 0080528864
Category : Mathematics
Languages : en
Pages : 469
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Book Description
These days computer-generated fractal patterns are everywhere, from squiggly designs on computer art posters to illustrations in the most serious of physics journals. Interest continues to grow among scientists and, rather surprisingly, artists and designers. This book provides visual demonstrations of complicated and beautiful structures that can arise in systems, based on simple rules. It also presents papers on seemingly paradoxical combinations of randomness and structure in systems of mathematical, physical, biological, electrical, chemical, and artistic interest. Topics include: iteration, cellular automata, bifurcation maps, fractals, dynamical systems, patterns of nature created through simple rules, and aesthetic graphics drawn from the universe of mathematics and art.Chaos and Fractals is divided into six parts: Geometry and Nature; Attractors; Cellular Automata, Gaskets, and Koch Curves; Mandelbrot, Julia and Other Complex Maps; Iterated Function Systems; and Computer Art.Additionally, information on the latest practical applications of fractals and on the use of fractals in commercial products such as the antennas and reaction vessels is presented. In short, fractals are increasingly finding application in practical products where computer graphics and simulations are integral to the design process. Each of the six sections has an introduction by the editor including the latest research, references, and updates in the field. This book is enhanced with numerous color illustrations, a comprehensive index, and the many computer program examples encourage reader involvement.
Author: C.A. Pickover
Publisher: Elsevier
ISBN: 0080528864
Category : Mathematics
Languages : en
Pages : 469
Get Book Here
Book Description
These days computer-generated fractal patterns are everywhere, from squiggly designs on computer art posters to illustrations in the most serious of physics journals. Interest continues to grow among scientists and, rather surprisingly, artists and designers. This book provides visual demonstrations of complicated and beautiful structures that can arise in systems, based on simple rules. It also presents papers on seemingly paradoxical combinations of randomness and structure in systems of mathematical, physical, biological, electrical, chemical, and artistic interest. Topics include: iteration, cellular automata, bifurcation maps, fractals, dynamical systems, patterns of nature created through simple rules, and aesthetic graphics drawn from the universe of mathematics and art.Chaos and Fractals is divided into six parts: Geometry and Nature; Attractors; Cellular Automata, Gaskets, and Koch Curves; Mandelbrot, Julia and Other Complex Maps; Iterated Function Systems; and Computer Art.Additionally, information on the latest practical applications of fractals and on the use of fractals in commercial products such as the antennas and reaction vessels is presented. In short, fractals are increasingly finding application in practical products where computer graphics and simulations are integral to the design process. Each of the six sections has an introduction by the editor including the latest research, references, and updates in the field. This book is enhanced with numerous color illustrations, a comprehensive index, and the many computer program examples encourage reader involvement.
Author: Gabriele A. Losa
Publisher: Birkhäuser
ISBN: 3034881193
Category : Mathematics
Languages : en
Pages : 354
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Book Description
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 provided stimulating contributions from the very topical field Fractals in Biology and Medicine. This volume highlights the growing power and efficacy of the fractal geometry in understanding how to analyze living phenomena and complex shapes.
Author: Oliver Linton
Publisher: eBook Partnership
ISBN: 191270613X
Category : Mathematics
Languages : en
Pages : 64
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Book Description
What are fractals? Why are they such fun? How do you make one? Why is a dripping tap not as random as it seems? What is chaos? Is the Mandelbrot Set really the most complex object in mathematics? In this beautifully illustrated book, fractal-hunter Oliver Linton takes us on a fascinating journey into the mathematics of fractals and chaos, diving into many kinds of self- similar structures to reveal some of the most recently discovered and intriguing patterns in science and nature. "e;Fascinating"e; FINANCIAL TIMES. "e;Beautiful"e; LONDON REVIEW OF BOOKS. "e;Rich and Artful"e; THE LANCET. "e;Genuinely mind-expanding"e; FORTEAN TIMES. "e;Excellent"e; NEW SCIENTIST. "e;Stunning"e; NEW YORK TIMES. Small books, big ideas.
Author: James B Bassingthwaighte
Publisher: Springer
ISBN: 1461475724
Category : Medical
Languages : en
Pages : 371
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Book Description
I know that most men, including those at ease with the problems of the greatest complexity, can seldom accept even the simplest and most obvious truth if it be such as would oblige them to admit the falsity of conclusions which they have delighted in explaining to colleagues, which they have proudly taught to others, and which they have woven, thread by thread, into the fabric of their lives. Joseph Ford quoting Tolstoy (Gleick, 1987) We are used to thinking that natural objects have a certain form and that this form is determined by a characteristic scale. If we magnify the object beyond this scale, no new features are revealed. To correctly measure the properties of the object, such as length, area, or volume, we measure it at a resolution finer than the characteristic scale of the object. We expect that the value we measure has a unique value for the object. This simple idea is the basis of the calculus, Euclidean geometry, and the theory of measurement. However, Mandelbrot (1977, 1983) brought to the world's attention that many natural objects simply do not have this preconceived form. Many of the structures in space and processes in time of living things have a very different form. Living things have structures in space and fluctuations in time that cannot be characterized by one spatial or temporal scale. They extend over many spatial or temporal scales.
Author: C.C. Barton
Publisher: Springer Science & Business Media
ISBN: 1489913971
Category : Technology & Engineering
Languages : en
Pages : 277
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Book Description
Fractals have changed the way we understand and study nature. This change has been brought about mainly by the work of B. B. Mandelbrot and his book The Fractal Geometry of Nature. Now here is a book that collects articles treating fractals in the earth sciences. The themes chosen span, as is appropriate for a discourse on fractals, many orders of magnitude; including earthquakes, ocean floor topography, fractures, faults, mineral crystallinity, gold and silver deposition. There are also chapters on dynamical processes that are fractal, such as rivers, earthquakes, and a paper on self-organized criticality. Many of the chapters discuss how to estimate fractal dimensions, Hurst exponents, and other scaling exponents. This book, in a way, represents a snapshot of a field in which fractals has brought inspiration and a fresh look at familiar subjects. New ideas and attempts to quantify the world we see around us are found throughout. Many of these ideas will grow and inspire further work, others will be superseded by new observations and insights, most probably with future contributions by the authors of these chapters.
Author: L. Pietronero
Publisher: Elsevier
ISBN: 0444598413
Category : Science
Languages : en
Pages : 489
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Book Description
Fractals in Physics
Author: Yurij Baryshev
Publisher: World Scientific
ISBN: 9789810248727
Category : Science
Languages : en
Pages : 412
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Book Description
In a simple manner, explains the frontiers of astronomy, how fractals appear in cosmic physics, offers a personal view of the history of the idea of self-similarity and of cosmological principles and presents the debate which illustrates how new concepts and deeper observations reveal unexpected aspects of Nature.
Author: Benoit Mandelbrot
Publisher: Springer Science & Business Media
ISBN: 9780387989938
Category : Mathematics
Languages : en
Pages : 672
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Book Description
This third volume of the Selected Works focusses on a detailed study of fraction Brownian motions. The fractal themes of "self-affinity" and "globality" are presented, while extensive introductory material, written especially for this book, precedes the papers and presents a number of striking new observations and conjectures. The mathematical tools so discussed will be valuable to diverse scientific communities.
Author: John L. Culliney
Publisher: University of Hawaii Press
ISBN: 0824866649
Category : Science
Languages : en
Pages : 257
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Book Description
Our universe, science reveals, began in utter simplicity, then evolved into burgeoning complexity. Starting with subatomic particles, dissimilar entities formed associations—binding, bonding, growing, branching, catalyzing, cooperating—as “self” joined “other” following universal laws with names such as gravity, chemical attraction, and natural selection. Ultimately life arose in a world of dynamic organic chemistry, and complexity exploded with wondrous new potential. Fast forward to human evolution, and a tension that had existed for billions of years now played out in an unprecedented arena of conscious calculation and cultural diversity. Cooperation interleaving with competition; intimacy oscillating with integrity—we dwell in a world where yin meets yang in human affairs on many levels. In The Fractal Self, John Culliney and David Jones uncover surprising intersections between science and philosophy. Connecting evidence from evolutionary science with early insights of Daoist and Buddhist thinkers, among others, they maintain that sagely behavior, envisioned in these ancient traditions, represents a pinnacle of human achievement emerging out of our evolutionary heritage. They identify an archetype, “the fractal self,” a person in any walk of life who cultivates a cooperative spirit. A fractal self is a sage in training, who joins others in common cause, leads from within, and achieves personal satisfaction in coordinating smooth performance of the group, team, or institution in which he or she is embedded. Fractal selves commonly operate with dedication and compassionate practice in the service of human society or in conserving our planet. But the competitive side of human nature is susceptible to greed and aggression. Self-aggrandizement, dictatorial power, and ego-driven enforcement of will are the goals of those following a self-serving path—individuals the authors identify as antisages. Terrorist leaders are an especially murderous breed, but aggrandizers can be found throughout business, religion, educational institutions, and governments. Humanity has reached an existential tipping point: will the horizon already in view expand with cooperative progress toward godlike emergent opportunities or contract in the thrall of corrupt oligarchs and tribal animosities? We have brought ourselves to a chaotic edge between immense promise and existential danger and are even now making our greatest choice.
Author: Antonio Di Ieva
Publisher: Springer
ISBN: 1493939955
Category : Medical
Languages : en
Pages : 583
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Book Description
Reviews the most intriguing applications of fractal analysis in neuroscience with a focus on current and future potential, limits, advantages, and disadvantages. Will bring an understanding of fractals to clinicians and researchers also if they do not have a mathematical background, and will serve as a good tool for teaching the translational applications of computational models to students and scholars of different disciplines. This comprehensive collection is organized in four parts: (1) Basics of fractal analysis; (2) Applications of fractals to the basic neurosciences; (3) Applications of fractals to the clinical neurosciences; (4) Analysis software, modeling and methodology.
