Fractal Dimensions
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A Random Walk Through Fractal Dimensions
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Author : Brian H. Kaye
language : en
Publisher: John Wiley & Sons
Release Date : 2008-07-11
A Random Walk Through Fractal Dimensions written by Brian H. Kaye and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-07-11 with Technology & Engineering categories.
Fractal geometry is revolutionizing the descriptive mathematics of applied materials systems. Rather than presenting a mathematical treatise, Brian Kaye demonstrates the power of fractal geometry in describing materials ranging from Swiss cheese to pyrolytic graphite. Written from a practical point of view, the author assiduously avoids the use of equations while introducing the reader to numerous interesting and challenging problems in subject areas ranging from geography to fine particle science. The second edition of this successful book provides up-to-date literature coverage of the use of fractal geometry in all areas of science. From reviews of the first edition: "...no stone is left unturned in the quest for applications of fractal geometry to fine particle problems....This book should provide hours of enjoyable reading to those wishing to become acquainted with the ideas of fractal geometry as applied to practical materials problems." MRS Bulletin
Fractal Dimension For Fractal Structures
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Author : Manuel Fernández-Martínez
language : en
Publisher: Springer
Release Date : 2019-04-23
Fractal Dimension For Fractal Structures written by Manuel Fernández-Martínez and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-23 with Mathematics categories.
This book provides a generalised approach to fractal dimension theory from the standpoint of asymmetric topology by employing the concept of a fractal structure. The fractal dimension is the main invariant of a fractal set, and provides useful information regarding the irregularities it presents when examined at a suitable level of detail. New theoretical models for calculating the fractal dimension of any subset with respect to a fractal structure are posed to generalise both the Hausdorff and box-counting dimensions. Some specific results for self-similar sets are also proved. Unlike classical fractal dimensions, these new models can be used with empirical applications of fractal dimension including non-Euclidean contexts. In addition, the book applies these fractal dimensions to explore long-memory in financial markets. In particular, novel results linking both fractal dimension and the Hurst exponent are provided. As such, the book provides a number of algorithms for properly calculating the self-similarity exponent of a wide range of processes, including (fractional) Brownian motion and Lévy stable processes. The algorithms also make it possible to analyse long-memory in real stocks and international indexes. This book is addressed to those researchers interested in fractal geometry, self-similarity patterns, and computational applications involving fractal dimension and Hurst exponent.
A Random Walk Through Fractal Dimensions
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Author : Brian Howard Kaye
language : en
Publisher: Weinheim [Germany] : VCH Verlagsgesellschaft
Release Date : 1989
A Random Walk Through Fractal Dimensions written by Brian Howard Kaye and has been published by Weinheim [Germany] : VCH Verlagsgesellschaft this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.
The aim of this book is both to stimulate interest in fractal geometry and to be useful as a first text to those who use fractal geometry in their work. It contains many suggestions for experiments, and tends to rely on graphic examples, rather than swamping the reader with equations and symbols.
Fractal Dimensions Of Networks
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Author : Eric Rosenberg
language : en
Publisher: Springer Nature
Release Date : 2020-07-07
Fractal Dimensions Of Networks written by Eric Rosenberg and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-07 with Computers categories.
Current interest in fractal dimensions of networks is the result of more than a century of previous research on dimensions. Fractal Dimensions of Networks ties the theory and methods for computing fractal dimensions of networks to the “classic” theory of dimensions of geometric objects. The goal of the book is to provide a unified treatment of fractal dimensions of sets and networks. Since almost all of the major concepts in fractal dimensions originated in the study of sets, the book achieves this goal by first clearly presenting, with an abundance of examples and illustrations, the theory and algorithms for sets, and then showing how the theory and algorithms have been applied to networks. Thus, the book presents the classical theory and algorithms for the box counting dimension for sets, and then presents the box counting dimension for networks. All the major fractal dimensions are studied, e.g., the correlation dimension, the information dimension, the Hausdorff dimension, the multifractal spectrum, as well as many lesser known dimensions. Algorithm descriptions are accompanied by worked examples, many applications of the methods are presented, and many exercises, ranging in difficulty from easy to research level, are included.
A Survey Of Fractal Dimensions Of Networks
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Author : Eric Rosenberg
language : en
Publisher: Springer
Release Date : 2018-05-29
A Survey Of Fractal Dimensions Of Networks written by Eric Rosenberg and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-29 with Computers categories.
Many different fractal dimensions have been proposed for networks. In A Survey of Fractal Dimensions of Networks the theory and computation of the most important of these dimensions are reviewed, including the box counting dimension, the correlation dimension, the mass dimension, the transfinite fractal dimension, the information dimension, the generalized dimensions (which provide a way to describe multifractals), and the sandbox method (for approximating the generalized dimensions). The book describes the use of diameter-based and radius-based boxes, and presents several heuristic methods for box counting, including greedy coloring, random sequential node burning, and a method for computing a lower bound. We also discuss very recent results on resolving ambiguity in the calculation of the information dimension and the generalized dimensions, and on the non-monotonicity of the generalized dimensions. Anyone interested in the theory and application of networks will want to read this Brief. This includes anyone studying, e.g., social networks, telecommunications networks, transportation networks, ecological networks, food chain networks, network models of the brain, or financial networks.
Fractals
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Author : G. Cherbit
language : en
Publisher:
Release Date : 1991-01-31
Fractals written by G. Cherbit and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-01-31 with Mathematics categories.
This text will be a valuable tool and reference work for all those interested in fractal forms and their properties. The past decade has seen an almost exponential amount of work done in the field of non-integral dimensions. Upon publication of Mandelbrot's Objets Fractals (1975), a great number of researchers understood the interest of fractals. Many tried, by means of the theory, to set up immediately useable tools, including the author, who opted for an experimental approach and developed instrumentation to explore the widest possible range in both time and space (time resolution of the laser spectroscopy of biomolecules). In this spirit, these expert researchers organized monthly ``Hausdorff seminars on the notion of non-integral dimension and its applications'' to tackle the problems confronting practical scientists. This work captures, with many illustrative examples, the main themes of each session.
The Fractal Dimension Of Architecture
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Author : Michael J. Ostwald
language : en
Publisher: Birkhäuser
Release Date : 2016-09-01
The Fractal Dimension Of Architecture written by Michael J. Ostwald and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-01 with Mathematics categories.
Fractal analysis is a method for measuring, analysing and comparing the formal or geometric properties of complex objects. In this book it is used to investigate eighty-five buildings that have been designed by some of the twentieth-century’s most respected and celebrated architects. Including designs by Le Corbusier, Eileen Gray, Frank Lloyd Wright, Robert Venturi, Frank Gehry, Peter Eisenman, Richard Meier and Kazuyo Sejima amongst others, this book uses mathematics to analyse arguments and theories about some of the world’s most famous designs. Starting with 625 reconstructed architectural plans and elevations, and including more than 200 specially prepared views of famous buildings, this book presents the results of the largest mathematical study ever undertaken into architectural design and the largest single application of fractal analysis presented in any field. The data derived from this study is used to test three overarching hypotheses about social, stylistic and personal trends in design, along with five celebrated arguments about twentieth-century architecture. Through this process the book offers a unique mathematical insight into the history and theory of design.
Fractal Dimensions For Poincare Recurrences
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Author : Valentin Afraimovich
language : en
Publisher: Elsevier
Release Date : 2006-06-21
Fractal Dimensions For Poincare Recurrences written by Valentin Afraimovich and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-21 with Science categories.
This book is devoted to an important branch of the dynamical systems theory : the study of the fine (fractal) structure of Poincare recurrences -instants of time when the system almost repeats its initial state. The authors were able to write an entirely self-contained text including many insights and examples, as well as providing complete details of proofs. The only prerequisites are a basic knowledge of analysis and topology. Thus this book can serve as a graduate text or self-study guide for courses in applied mathematics or nonlinear dynamics (in the natural sciences). Moreover, the book can be used by specialists in applied nonlinear dynamics following the way in the book. The authors applied the mathematical theory developed in the book to two important problems: distribution of Poincare recurrences for nonpurely chaotic Hamiltonian systems and indication of synchronization regimes in coupled chaotic individual systems. * Portions of the book were published in an article that won the title "month's new hot paper in the field of Mathematics" in May 2004 * Rigorous mathematical theory is combined with important physical applications * Presents rules for immediate action to study mathematical models of real systems * Contains standard theorems of dynamical systems theory
Fractal Dimensions
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Author : Eric Hammel
language : en
Publisher: IPS Books
Release Date : 2014-08-22
Fractal Dimensions written by Eric Hammel and has been published by IPS Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-22 with Art categories.
The concept behind fractal geometry is extremely difficult to explain . . . but easy to see and enjoy. Eric Hammel, a professional author of military history books, is unable to explain fractals in a way that will be clear to anyone else, but most mathematicians canÕt explain fractals in language most people can understand. The simplest explanation is that fractals are graphic representations of high-order mathematical formulas that repeat patterns to infinity. DonÕt get hung up on the math. ItÕs really all in the seeing. Like Volumes 1 through 4 of Eric HammelÕs Fractal Dimensions, Volume 5 is filled with one hundred examples representing many types of fractals. The differences between and among fractal artists using the same array of fractal-generating software is the same as the differences between and among all portrait artists or between and among all landscape artists using oil paint, chalk, watercolors, charcoal, even fingers. It all comes down to the unique mindÕs eye the artist brings to the game and what he does to improve or transform the art once the fractal-generating software has been sufficiently exploited. For all that, all a lay person really needs to appreciate fractals in their infinite varieties is a collection of fractal art to peruse, to get lost in for awhile, and their own preferences for art. No two fractal artists will see or exploit the same fractal formula the same way. What we offer here is simply what one fractal artist has been able to see, and what he alone decided he wants to share.
Curves And Fractal Dimension
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Author : Claude Tricot
language : en
Publisher: Springer Science & Business Media
Release Date : 1994-11-18
Curves And Fractal Dimension written by Claude Tricot and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-11-18 with Mathematics categories.
Written for mathematicians, engineers, and researchers in experimental science, as well as anyone interested in fractals, this book explains the geometrical and analytical properties of trajectories, aggregate contours, geographical coastlines, profiles of rough surfaces, and other curves of finite and fractal length. The approach is by way of precise definitions from which properties are deduced and applications and computational methods are derived. Written without the traditional heavy symbolism of mathematics texts, this book requires two years of calculus while also containing material appropriate for graduate coursework in curve analysis and/or fractal dimension.