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 (4.5 / 5.0) The authors present an unusual attempt to publicize the field of Complex Dynamics, an exciting mathematical discipline of respectable tradition that recently sprang into new life under the impact of modern computer graphics. Where previous generations of scientists had to develop their own inner eye to perceive the abstract aesthetics of their work, the astonding pictures assembled here invite the reader to share in a new mathematical experience, to revel in the charm of fractal frontiers. 184 illustrations in 211 parts, 88 in color.
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$32.94 |
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 (5.0 / 5.0) Fractal structures are found everywhere in nature, and as a consequence anomalous diffusion has far reaching implications in a host of phenomena. This book describes diffusion and transport in disordered media such as fractals, porous rocks and random resistor networks. Part I contains material of general interest to statistical physics: fractals, percolation theory, regular random walks and diffusion, continuous time random walks and Levy walks, and flights. Part II covers anomalous diffusion in fractals and disordered media, while Part III serves as an introduction to the kinetics of diffusion-limited reactions. Part IV discusses the problem of diffusion-limited coalescence in one dimension. This book will be of particular interest to researchers requiring a clear introduction to the field. It will also be a valuable source to graduate students studying in areas of physics, chemistry, and engineering.
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$57.95 |
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 (1.0 / 5.0) Where Medicine Went Wrong explores how the idea of an average value has been misapplied to medical phenomena, distorted understanding and lead to flawed medical decisions. Through new insights into the science of complexity, traditional physiology is replaced with fractal physiology, in which variability is more indicative of health than is an average. The capricious nature of physiological systems is made conceptually manageable by smoothing over fluctuations and thinking in terms of averages. But these variations in such aspects as heart rate, breathing and walking are much more susceptible to the early influence of disease than are averages. It may be useful to quote from the late Stephen Jay Gould s book Full House on the errant nature of averages: ... our culture encodes a strong bias either to neglect or ignore variation. We tend to focus instead on measures of central tendency, and as a result we make some terrible mistakes, often with considerable practical import. Dr West has quantified this observation and make it useful for the diagnosis of disease.
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$57.99 |
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(4.5 / 5.0) Benoit Mandelbrot discovered what is now called the M-Set in the early seventies and coined the term fractal to describe the geometry behind it. The power and the beauty of fractals were only capable of being seen with the advent of computers, which become psychedelic windows on the infinite when using simple fractal equations. In 1992 Nigel Lesmoir-Gordon made the TV documentary, The Colors of Infinity about the Mandelbrot Set and fractals, which has since been seen right round the world. Nigel s enthusiasm brought together a dream team of contributors for the film who all now contribute to the book tracking how fractals have developed since the film was made. Sir Arthur C Clarke presented the film and in the book gives a lucidly simple account of the mathematics of the M-Set. Benoit Mandelbrot, the Belgian mathematician explains how it began. Professor Michael Barnsley, the computer graphics researcher who developed fractal image compression technology, explains the applications of the breakthroughs. Professor Ian Stewart, author of Does God Play Dice? adds his insights into the beautifully simple equation that gives birth to fractals. Two of the most interesting applications of fractal geometry, reflected by the two new contributors to the book, are to the Internet and to the Stock Market. Dr Gary Flake, Chief Technology Officer at Overture, the leading provider of commercial search on the Internet and just taken over by Yahoo for 1.6 billion dollars, discusses the profoundly fractal nature of the Web in his article: The Self-ish Web. Robert Prechter Jr is President of Elliott Wave International, Inc. and founder of the Socionomics Institute. His latest title is Socionomics: The Science of History and Social Prediction (2003). He writes about how fractals can help us understand the oscillations of stock markets. In the back of the book is a DVD of the original documentary with soundtrack by David Gilmour of Pink Floyd PLUS a 30-minute fractal animation to the music of members of Quintessence.
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$89.00 |
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 (2.0 / 5.0) We are surrounded by order that-until now-physics has been unable to explain.
The spread of veins in the back of our hands mirrors the spread of branches on a tree; fern fronds bear a resemblance to the outline of fjords; the best-loved classical music echoes the patterns of our heartbeats. The theory of Universality is using fractal patterns to explain much of the world around us. Could it be that the same laws that govern systems in their critical states also govern some of the most unpredictable events such as earthquakes, avalanches, the growth of cities and stock market crashes-even the way businesses are run and the way fashions come and go? Is there a common principle, a universal affinity that binds us to the forces of nature? A consensus is emerging on how complex structures grow and sustain themselves; phenomena that were once thought to be unique now appear to have a great deal in common. Mark Ward examines these theories, explores how they fit into an age-long quest to discover how the universe works, delves into their possible limitations and asks what we can do with this new knowledge. While identifying patterns does not mean that we can always predict what will happen next, some of the trends scientists are noticing prove that life is not a series of random events. Universality deepens our understanding of natural phenomena and our place in the physical world. We are surrounded by order that-until now-physics has been unable to explain. The spread of veins in the back of our hands mirrors the spread of branches on a tree; fern fronds bear a resemblance to the outline of fjords; the best-loved classical music echoes the patterns of our heartbeats. The theory of Universality is using fractal patterns to explain much of the world around us. Could it be that the same laws that govern systems in their critical states also govern some of the most unpredictable events such as earthquakes, avalanches, the growth of cities and stock market crashes-even the way businesses are run and the way fashions come and go? Is there a common principle, a universal affinity that binds us to the forces of nature? A consensus is emerging on how complex structures grow and sustain themselves; phenomena that were once thought to be unique now appear to have a great deal in common. Mark Ward examines these theories, explores how they fit into an age-long quest to discover how the universe works, delves into their possible limitations and asks what we can do with this new knowledge. While identifying patterns does not mean that we can always predict what will happen next, some of the trends scientists are noticing prove that life is not a series of random events. Universality deepens our understanding of natural phenomena and our place in the physical world.
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$9.50 |
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Provides an Intuitive View of Various Ecological Patterns and Processes Ecologists sometimes have a less-than-rigorous background in quantitative methods, yet research within this broad field is becoming increasingly mathematical. Written in a step-by-step fashion, Fractals and Multifractals in Ecology and Aquatic Science provides scientists with a basic understanding of fractals and multifractals and the techniques for utilizing them when analyzing ecological phenomenon. With illustrations, tables, and graphs on virtually every page – several in color – this book is a comprehensive source of state-of-the-art ecological scaling and multiscaling methods at temporal and spatial scales, respectfully ranging from seconds to months and from millimeters to thousands of kilometers. It illustrates most of the data analysis techniques with real case studies often based on original findings. It also incorporates descriptions of current and new numerical techniques to analyze and deepen understanding of ecological situations and their solutions. Includes a Wealth of Applications and Examples This book also includes nonlinear analysis techniques and the application of concepts from chaos theory to problems of spatial and temporal patterns in ecological systems. Unlike other books on the subject, Fractals and Multifractals in Ecology and Aquatic Science is readily accessible to researchers in a variety of fields, such as microbiology, biology, ecology, hydrology, geology, oceanography, social sciences, and finance, regardless of their mathematical backgrounds. This volume demystifies the mathematical methods, many of which are often regarded as too complex, and allows the reader to access new and promising concepts, procedures, and related results.
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$74.31 |
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Number theory, spectral geometry, and fractal geometry are interlinked in this in-depth study of the vibrations of fractal strings, that is, one-dimensional drums with fractal boundary. Key Features: - The Riemann hypothesis is given a natural geometric reformulation in the context of vibrating fractal strings - Complex dimensions of a fractal string, defined as the poles of an associated zeta function, are studied in detail, then used to understand the oscillations intrinsic to the corresponding fractal geometries and frequency spectra - Explicit formulas are extended to apply to the geometric, spectral, and dynamic zeta functions associated with a fractal - Examples of such formulas include Prime Orbit Theorem with error term for self-similar flows, and a tube formula - The method of diophantine approximation is used to study self-similar strings and flows - Analytical and geometric methods are used to obtain new results about the vertical distribution of zeros of number-theoretic and other zeta functions Throughout new results are examined. The final chapter gives a new definition of fractality as the presence of nonreal complex dimensions with positive real parts. The significant studies and problems illuminated in this work may be used in a classroom setting at the graduate level. Fractal Geometry, Complex Dimensions and Zeta Functions will appeal to students and researchers in number theory, fractal geometry, dynamical systems, spectral geometry, and mathematical physics.
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$13.74 |
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 (2.5 / 5.0) Multifractal Based Network Traffic Modeling provides an overview of existing broadband traffic modeling based on the Poisson process and its variants like the MM1 models. It also provides very good coverage of models based on self-similar processes. Throughout the book, the authors have focused on the problem of broadband traffic modeling keeping in mind long range dependencies in broadband traffic. Graduate students, researchers, and individuals new to the areas of teletraffic modeling and communication network engineering will find this work especially helpful. The book could also be used as a textbook for a graduate level course on Teletraffic Modeling.
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$5.73 |
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(5.0 / 5.0) Cathodic arcs are among the longest studied yet least understood objects in science. Plasma-generating, tiny spots appear on the cathode; they are highly dynamic and hard to control. With an approach emphasizing the fractal character of cathode spots, strongly fluctuating plasma properties are described such as the presence of multiply charged ions that move with supersonic velocity. Richly illustrated, the book also deals with practical issues, such as arc source construction, macroparticle removal, and the synthesis of dense, well adherent coatings. The book spans a bridge from plasma physics to coatings technology based on energetic condensation, appealing to scientists, practitioners and graduate students alike.
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$103.06 |
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 (4.0 / 5.0) The fractal cuts in this text are used to create attractive pop-up cards. Each is made from a single sheet of white paper cut according to a fractal rule and glued within a brightly coloured cover.
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$199.95 |