Fractal Dimensions of Networks

Download Fractal Dimensions of Networks PDF Online Free

Author :
Publisher : Springer Nature
ISBN 13 : 303043169X
Total Pages : 530 pages
Book Rating : 4.0/5 (34 download)

DOWNLOAD NOW!


Book Synopsis Fractal Dimensions of Networks by : Eric Rosenberg

Download or read book Fractal Dimensions of Networks written by Eric Rosenberg and published by Springer Nature. This book was released on 2020-07-07 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Fractal Dimension for Fractal Structures

Download Fractal Dimension for Fractal Structures PDF Online Free

Author :
Publisher : Springer
ISBN 13 : 3030166457
Total Pages : 217 pages
Book Rating : 4.0/5 (31 download)

DOWNLOAD NOW!


Book Synopsis Fractal Dimension for Fractal Structures by : Manuel Fernández-Martínez

Download or read book Fractal Dimension for Fractal Structures written by Manuel Fernández-Martínez and published by Springer. This book was released on 2019-04-23 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Fractal Dimension of Architecture

Download The Fractal Dimension of Architecture PDF Online Free

Author :
Publisher : Birkhäuser
ISBN 13 : 3319324268
Total Pages : 429 pages
Book Rating : 4.3/5 (193 download)

DOWNLOAD NOW!


Book Synopsis The Fractal Dimension of Architecture by : Michael J. Ostwald

Download or read book The Fractal Dimension of Architecture written by Michael J. Ostwald and published by Birkhäuser. This book was released on 2016-09-01 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

A Random Walk Through Fractal Dimensions

Download A Random Walk Through Fractal Dimensions PDF Online Free

Author :
Publisher : John Wiley & Sons
ISBN 13 : 3527615989
Total Pages : 452 pages
Book Rating : 4.5/5 (276 download)

DOWNLOAD NOW!


Book Synopsis A Random Walk Through Fractal Dimensions by : Brian H. Kaye

Download or read book A Random Walk Through Fractal Dimensions written by Brian H. Kaye and published by John Wiley & Sons. This book was released on 2008-07-11 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Geometry, Complex Dimensions and Zeta Functions

Download Fractal Geometry, Complex Dimensions and Zeta Functions PDF Online Free

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 1461421764
Total Pages : 583 pages
Book Rating : 4.4/5 (614 download)

DOWNLOAD NOW!


Book Synopsis Fractal Geometry, Complex Dimensions and Zeta Functions by : Michel L. Lapidus

Download or read book Fractal Geometry, Complex Dimensions and Zeta Functions written by Michel L. Lapidus and published by Springer Science & Business Media. This book was released on 2012-09-20 with total page 583 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. Throughout Geometry, Complex Dimensions and Zeta Functions, Second Edition, new results are examined and a new definition of fractality as the presence of nonreal complex dimensions with positive real parts is presented. The new final chapter discusses several new topics and results obtained since the publication of the first edition.

Measure, Topology, and Fractal Geometry

Download Measure, Topology, and Fractal Geometry PDF Online Free

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 1475741340
Total Pages : 252 pages
Book Rating : 4.4/5 (757 download)

DOWNLOAD NOW!


Book Synopsis Measure, Topology, and Fractal Geometry by : Gerald A. Edgar

Download or read book Measure, Topology, and Fractal Geometry written by Gerald A. Edgar and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "In the world of mathematics, the 1980's might well be described as the "decade of the fractal". Starting with Benoit Mandelbrot's remarkable text The Fractal Geometry of Nature, there has been a deluge of books, articles and television programmes about the beautiful mathematical objects, drawn by computers using recursive or iterative algorithms, which Mandelbrot christened fractals. Gerald Edgar's book is a significant addition to this deluge. Based on a course given to talented high- school students at Ohio University in 1988, it is, in fact, an advanced undergraduate textbook about the mathematics of fractal geometry, treating such topics as metric spaces, measure theory, dimension theory, and even some algebraic topology. However, the book also contains many good illustrations of fractals (including 16 color plates), together with Logo programs which were used to generate them. ... Here then, at last, is an answer to the question on the lips of so many: 'What exactly is a fractal?' I do not expect many of this book's readers to achieve a mature understanding of this answer to the question, but anyone interested in finding out about the mathematics of fractal geometry could not choose a better place to start looking." #Mathematics Teaching#1

Curves and Fractal Dimension

Download Curves and Fractal Dimension PDF Online Free

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 9780387940953
Total Pages : 362 pages
Book Rating : 4.9/5 (49 download)

DOWNLOAD NOW!


Book Synopsis Curves and Fractal Dimension by : Claude Tricot

Download or read book Curves and Fractal Dimension written by Claude Tricot and published by Springer Science & Business Media. This book was released on 1994-11-18 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Assouad Dimension and Fractal Geometry

Download Assouad Dimension and Fractal Geometry PDF Online Free

Author :
Publisher : Cambridge University Press
ISBN 13 : 1108478654
Total Pages : 287 pages
Book Rating : 4.1/5 (84 download)

DOWNLOAD NOW!


Book Synopsis Assouad Dimension and Fractal Geometry by : Jonathan M. Fraser

Download or read book Assouad Dimension and Fractal Geometry written by Jonathan M. Fraser and published by Cambridge University Press. This book was released on 2020-10-29 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first thorough treatment of the Assouad dimension in fractal geometry, with applications to many fields within pure mathematics.

Fractals

Download Fractals PDF Online Free

Author :
Publisher :
ISBN 13 :
Total Pages : 280 pages
Book Rating : 4.:/5 (319 download)

DOWNLOAD NOW!


Book Synopsis Fractals by : G. Cherbit

Download or read book Fractals written by G. Cherbit and published by . This book was released on 1991-01-31 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

A Survey of Fractal Dimensions of Networks

Download A Survey of Fractal Dimensions of Networks PDF Online Free

Author :
Publisher : Springer
ISBN 13 : 3319900471
Total Pages : 87 pages
Book Rating : 4.3/5 (199 download)

DOWNLOAD NOW!


Book Synopsis A Survey of Fractal Dimensions of Networks by : Eric Rosenberg

Download or read book A Survey of Fractal Dimensions of Networks written by Eric Rosenberg and published by Springer. This book was released on 2018-05-29 with total page 87 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Fractal Dimensions for Poincare Recurrences

Download Fractal Dimensions for Poincare Recurrences PDF Online Free

Author :
Publisher : Elsevier
ISBN 13 : 0080462391
Total Pages : 258 pages
Book Rating : 4.0/5 (84 download)

DOWNLOAD NOW!


Book Synopsis Fractal Dimensions for Poincare Recurrences by : Valentin Afraimovich

Download or read book Fractal Dimensions for Poincare Recurrences written by Valentin Afraimovich and published by Elsevier. This book was released on 2006-06-21 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Galileo Unbound

Download Galileo Unbound PDF Online Free

Author :
Publisher : Oxford University Press
ISBN 13 : 0192528505
Total Pages : 384 pages
Book Rating : 4.1/5 (925 download)

DOWNLOAD NOW!


Book Synopsis Galileo Unbound by : David D. Nolte

Download or read book Galileo Unbound written by David D. Nolte and published by Oxford University Press. This book was released on 2018-07-12 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Galileo Unbound traces the journey that brought us from Galileo's law of free fall to today's geneticists measuring evolutionary drift, entangled quantum particles moving among many worlds, and our lives as trajectories traversing a health space with thousands of dimensions. Remarkably, common themes persist that predict the evolution of species as readily as the orbits of planets or the collapse of stars into black holes. This book tells the history of spaces of expanding dimension and increasing abstraction and how they continue today to give new insight into the physics of complex systems. Galileo published the first modern law of motion, the Law of Fall, that was ideal and simple, laying the foundation upon which Newton built the first theory of dynamics. Early in the twentieth century, geometry became the cause of motion rather than the result when Einstein envisioned the fabric of space-time warped by mass and energy, forcing light rays to bend past the Sun. Possibly more radical was Feynman's dilemma of quantum particles taking all paths at once — setting the stage for the modern fields of quantum field theory and quantum computing. Yet as concepts of motion have evolved, one thing has remained constant, the need to track ever more complex changes and to capture their essence, to find patterns in the chaos as we try to predict and control our world.

The Fractal Geometry of Nature

Download The Fractal Geometry of Nature PDF Online Free

Author :
Publisher : Echo Point Books & Media, LLC
ISBN 13 : 9781648370410
Total Pages : 0 pages
Book Rating : 4.3/5 (74 download)

DOWNLOAD NOW!


Book Synopsis The Fractal Geometry of Nature by : Benoit Mandelbrot

Download or read book The Fractal Geometry of Nature written by Benoit Mandelbrot and published by Echo Point Books & Media, LLC. This book was released on 2021-07-16 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written in a style that is accessible to a wide audience, The Fractal Geometry of Nature inspired popular interest in this emerging field. Mandelbrot's unique style, and rich illustrations will inspire readers of all backgrounds.

Fractals

Download Fractals PDF Online Free

Author :
Publisher : Echo Point Books & Media
ISBN 13 : 9781635619027
Total Pages : 384 pages
Book Rating : 4.6/5 (19 download)

DOWNLOAD NOW!


Book Synopsis Fractals by : Benoit Mandelbrot

Download or read book Fractals written by Benoit Mandelbrot and published by Echo Point Books & Media. This book was released on 2020-02-25 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discover the Hidden Mathematics of Modern Geometry Fractals, the never-ending geometric-mathematical patterns existing throughout nature, are revealed in the shapes of continents, galaxies, snowflakes, and grains of sand. In this fascinating and seminal volume, renowned pioneering-mathematician Benoit B. Mandelbrot explains his work on fractal geometry, mathematically translating the description of these complex shapes of nature. Until Mandelbrot developed the concept of fractal geometry in the 1960s and 70s, most mathematicians believed these irregular shapes were too fragmented and amorphous to be described mathematically. Mandelbrot's revolutionary concept brought order to a variety of seemingly unsolvable problems in physics, biology, and financial markets. Broad in application, this groundbreaking work will inform not just mathematicians, but anyone that appreciates the natural elegance of patterns made manifest. Featuring illustrations of mathematically defined shapes, Mandelbrot describes how geometric patterns relate to every aspect of the physical world around us.

Fractal Physiology

Download Fractal Physiology PDF Online Free

Author :
Publisher : Springer
ISBN 13 : 1461475724
Total Pages : 371 pages
Book Rating : 4.4/5 (614 download)

DOWNLOAD NOW!


Book Synopsis Fractal Physiology by : James B Bassingthwaighte

Download or read book Fractal Physiology written by James B Bassingthwaighte and published by Springer. This book was released on 2013-05-27 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Handbook of Computability and Complexity in Analysis

Download Handbook of Computability and Complexity in Analysis PDF Online Free

Author :
Publisher : Springer Nature
ISBN 13 : 3030592340
Total Pages : 427 pages
Book Rating : 4.0/5 (35 download)

DOWNLOAD NOW!


Book Synopsis Handbook of Computability and Complexity in Analysis by : Vasco Brattka

Download or read book Handbook of Computability and Complexity in Analysis written by Vasco Brattka and published by Springer Nature. This book was released on 2021-06-04 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computable analysis is the modern theory of computability and complexity in analysis that arose out of Turing's seminal work in the 1930s. This was motivated by questions such as: which real numbers and real number functions are computable, and which mathematical tasks in analysis can be solved by algorithmic means? Nowadays this theory has many different facets that embrace topics from computability theory, algorithmic randomness, computational complexity, dynamical systems, fractals, and analog computers, up to logic, descriptive set theory, constructivism, and reverse mathematics. In recent decades computable analysis has invaded many branches of analysis, and researchers have studied computability and complexity questions arising from real and complex analysis, functional analysis, and the theory of differential equations, up to (geometric) measure theory and topology. This handbook represents the first coherent cross-section through most active research topics on the more theoretical side of the field. It contains 11 chapters grouped into parts on computability in analysis; complexity, dynamics, and randomness; and constructivity, logic, and descriptive complexity. All chapters are written by leading experts working at the cutting edge of the respective topic. Researchers and graduate students in the areas of theoretical computer science and mathematical logic will find systematic introductions into many branches of computable analysis, and a wealth of information and references that will help them to navigate the modern research literature in this field.

Fractal Concepts in Condensed Matter Physics

Download Fractal Concepts in Condensed Matter Physics PDF Online Free

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 9783540050445
Total Pages : 228 pages
Book Rating : 4.0/5 (54 download)

DOWNLOAD NOW!


Book Synopsis Fractal Concepts in Condensed Matter Physics by : Tsuneyoshi Nakayama

Download or read book Fractal Concepts in Condensed Matter Physics written by Tsuneyoshi Nakayama and published by Springer Science & Business Media. This book was released on 2003-07-11 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concisely and clearly written by two foremost scientists, this book provides a self-contained introduction to the basic concepts of fractals and demonstrates their use in a range of topics. The authors’ unified description of different dynamic problems makes the book extremely accessible.