Fractal Geometry
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Measure Topology And Fractal Geometry
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Author : Gerald A Edgar
language : en
Publisher: Springer
Release Date : 1990
Measure Topology And Fractal Geometry written by Gerald A Edgar and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.
This book provides the mathematics necessary for the study of fractal geometry. It includes background material on metric topology and measure theory and also covers topological and fractal dimension, including the Hausdorff dimension. Furthermore, the book contains a complete discussion of self-similarity as well as the more general "graph self-similarity."
The Fractal Geometry Of Nature
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Author : Benoit Mandelbrot
language : en
Publisher: Echo Point Books & Media, LLC
Release Date : 2021-07-16
The Fractal Geometry Of Nature written by Benoit Mandelbrot and has been published by Echo Point Books & Media, LLC this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-16 with categories.
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.
Lectures On Fractal Geometry And Dynamical Systems
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Author : Ya. B. Pesin
language : en
Publisher: American Mathematical Soc.
Release Date : 2009
Lectures On Fractal Geometry And Dynamical Systems written by Ya. B. Pesin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
Both fractal geometry and dynamical systems have a long history of development and have provided fertile ground for many great mathematicians and much deep and important mathematics. These two areas interact with each other and with the theory of chaos in a fundamental way: many dynamical systems (even some very simple ones) produce fractal sets, which are in turn a source of irregular 'chaotic' motions in the system. This book is an introduction to these two fields, with an emphasis on the relationship between them. The first half of the book introduces some of the key ideas in fractal geometry and dimension theory - Cantor sets, Hausdorff dimension, box dimension - using dynamical notions whenever possible, particularly one-dimensional Markov maps and symbolic dynamics. Various techniques for computing Hausdorff dimension are shown, leading to a discussion of Bernoulli and Markov measures and of the relationship between dimension, entropy, and Lyapunov exponents. In the second half of the book some examples of dynamical systems are considered and various phenomena of chaotic behaviour are discussed, including bifurcations, hyperbolicity, attractors, horseshoes, and intermittent and persistent chaos. These phenomena are naturally revealed in the course of our study of two real models from science - the FitzHugh - Nagumo model and the Lorenz system of differential equations. This book is accessible to undergraduate students and requires only standard knowledge in calculus, linear algebra, and differential equations. Elements of point set topology and measure theory are introduced as needed. This book is a result of the MASS course in analysis at Penn State University in the fall semester of 2008.
The Fractal Geometry Of The Brain
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Author : Antonio Di Ieva
language : en
Publisher: Springer
Release Date : 2016-08-03
The Fractal Geometry Of The Brain written by Antonio Di Ieva and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-03 with Medical categories.
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.
Fractal Geometry Complex Dimensions And Zeta Functions
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Author : Michel Lapidus
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-20
Fractal Geometry Complex Dimensions And Zeta Functions written by Michel Lapidus 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 2012-09-20 with Mathematics categories.
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.
Fractal Geometry In Architecture And Design
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Author : Carl Bovill
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-11
Fractal Geometry In Architecture And Design written by Carl Bovill 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 2013-03-11 with Mathematics categories.
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.
Fractal Geometry
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Author : Kenneth Falconer
language : en
Publisher: John Wiley & Sons
Release Date : 2014-02-03
Fractal Geometry written by Kenneth Falconer 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 2014-02-03 with Mathematics categories.
The seminal text on fractal geometry for students and researchers: extensively revised and updated with new material, notes and references that reflect recent directions. Interest in fractal geometry continues to grow rapidly, both as a subject that is fascinating in its own right and as a concept that is central to many areas of mathematics, science and scientific research. Since its initial publication in 1990 Fractal Geometry: Mathematical Foundations and Applications has become a seminal text on the mathematics of fractals. The book introduces and develops the general theory and applications of fractals in a way that is accessible to students and researchers from a wide range of disciplines. Fractal Geometry: Mathematical Foundations and Applications is an excellent course book for undergraduate and graduate students studying fractal geometry, with suggestions for material appropriate for a first course indicated. The book also provides an invaluable foundation and reference for researchers who encounter fractals not only in mathematics but also in other areas across physics, engineering and the applied sciences. Provides a comprehensive and accessible introduction to the mathematical theory and applications of fractals Carefully explains each topic using illustrative examples and diagrams Includes the necessary mathematical background material, along with notes and references to enable the reader to pursue individual topics Features a wide range of exercises, enabling readers to consolidate their understanding Supported by a website with solutions to exercises and additional material www.wileyeurope.com/fractal Leads onto the more advanced sequel Techniques in Fractal Geometry (also by Kenneth Falconer and available from Wiley)
Fractal Geometry And Number Theory
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Author : Michel L. Lapidus
language : en
Publisher: Springer Science & Business Media
Release Date : 2000
Fractal Geometry And Number Theory written by Michel L. Lapidus 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 2000 with Mathematics categories.
A fractal drum is a bounded open subset of R. m with a fractal boundary. A difficult problem is to describe the relationship between the shape (geo metry) of the drum and its sound (its spectrum). In this book, we restrict ourselves to the one-dimensional case of fractal strings, and their higher dimensional analogues, fractal sprays. We develop a theory of complex di mensions of a fractal string, and we study how these complex dimensions relate the geometry with the spectrum of the fractal string. We refer the reader to [Berrl-2, Lapl-4, LapPol-3, LapMal-2, HeLapl-2] and the ref erences therein for further physical and mathematical motivations of this work. (Also see, in particular, Sections 7. 1, 10. 3 and 10. 4, along with Ap pendix B. ) In Chapter 1, we introduce the basic object of our research, fractal strings (see [Lapl-3, LapPol-3, LapMal-2, HeLapl-2]). A 'standard fractal string' is a bounded open subset of the real line. Such a set is a disjoint union of open intervals, the lengths of which form a sequence which we assume to be infinite. Important information about the geometry of . c is contained in its geometric zeta function (c(8) = L lj. j=l 2 Introduction We assume throughout that this function has a suitable meromorphic ex tension. The central notion of this book, the complex dimensions of a fractal string . c, is defined as the poles of the meromorphic extension of (c.
Fractal Geometry In Digital Imaging
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Author : Martin J. Turner
language : en
Publisher: Academic Press
Release Date : 1998-06-23
Fractal Geometry In Digital Imaging written by Martin J. Turner and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-06-23 with Computers categories.
This book is concerned with the theory and application of fractal geometry in digital imaging. Throughout the book, a series of new approaches to defining fractals are illustrated, such as the analysis of the fractal power spectrum and the use of fractional differentials. Several new algorithms and applications are also discussed and applied to real life images. Fractal Geometry in Digital imaging will appeal to postgraduates, researchers and practitioners in image processing, mathematics and computing, information technology and engineering.
Fractal Geometry
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Author : Kenneth Falconer
language : en
Publisher: John Wiley & Sons
Release Date : 2004-01-09
Fractal Geometry written by Kenneth Falconer 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 2004-01-09 with Mathematics categories.
Since its original publication in 1990, Kenneth Falconer's Fractal Geometry: Mathematical Foundations and Applications has become a seminal text on the mathematics of fractals. It introduces the general mathematical theory and applications of fractals in a way that is accessible to students from a wide range of disciplines. This new edition has been extensively revised and updated. It features much new material, many additional exercises, notes and references, and an extended bibliography that reflects the development of the subject since the first edition. * Provides a comprehensive and accessible introduction to the mathematical theory and applications of fractals. * Each topic is carefully explained and illustrated by examples and figures. * Includes all necessary mathematical background material. * Includes notes and references to enable the reader to pursue individual topics. * Features a wide selection of exercises, enabling the reader to develop their understanding of the theory. * Supported by a Web site featuring solutions to exercises, and additional material for students and lecturers. Fractal Geometry: Mathematical Foundations and Applications is aimed at undergraduate and graduate students studying courses in fractal geometry. The book also provides an excellent source of reference for researchers who encounter fractals in mathematics, physics, engineering, and the applied sciences. Also by Kenneth Falconer and available from Wiley: Techniques in Fractal Geometry ISBN 0-471-95724-0