Geometry And Analysis Of Fractals
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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 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.
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.
Geometry And Analysis Of Fractals
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Author : De-Jun Feng
language : en
Publisher: Springer
Release Date : 2014-08-01
Geometry And Analysis Of Fractals written by De-Jun Feng and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-01 with Mathematics categories.
This volume collects thirteen expository or survey articles on topics including Fractal Geometry, Analysis of Fractals, Multifractal Analysis, Ergodic Theory and Dynamical Systems, Probability and Stochastic Analysis, written by the leading experts in their respective fields. The articles are based on papers presented at the International Conference on Advances on Fractals and Related Topics, held on December 10-14, 2012 at the Chinese University of Hong Kong. The volume offers insights into a number of exciting, cutting-edge developments in the area of fractals, which has close ties to and applications in other areas such as analysis, geometry, number theory, probability and mathematical physics.
Analysis On Fractals
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Author : Jun Kigami
language : en
Publisher: Cambridge University Press
Release Date : 2001-06-07
Analysis On Fractals written by Jun Kigami and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-06-07 with Mathematics categories.
This book covers analysis on fractals, a developing area of mathematics which focuses on the dynamical aspects of fractals, such as heat diffusion on fractals and the vibration of a material with fractal structure. The book provides a self-contained introduction to the subject, starting from the basic geometry of self-similar sets and going on to discuss recent results, including the properties of eigenvalues and eigenfunctions of the Laplacians, and the asymptotical behaviors of heat kernels on self-similar sets. Requiring only a basic knowledge of advanced analysis, general topology and measure theory, this book will be of value to graduate students and researchers in analysis and probability theory. It will also be useful as a supplementary text for graduate courses covering fractals.
Ergodic Theory And Fractal Geometry
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Author : Hillel Furstenberg
language : en
Publisher: American Mathematical Society
Release Date : 2014-08-08
Ergodic Theory And Fractal Geometry written by Hillel Furstenberg and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-08 with Mathematics categories.
Fractal geometry represents a radical departure from classical geometry, which focuses on smooth objects that "straighten out" under magnification. Fractals, which take their name from the shape of fractured objects, can be characterized as retaining their lack of smoothness under magnification. The properties of fractals come to light under repeated magnification, which we refer to informally as "zooming in". This zooming-in process has its parallels in dynamics, and the varying "scenery" corresponds to the evolution of dynamical variables. The present monograph focuses on applications of one branch of dynamics--ergodic theory--to the geometry of fractals. Much attention is given to the all-important notion of fractal dimension, which is shown to be intimately related to the study of ergodic averages. It has been long known that dynamical systems serve as a rich source of fractal examples. The primary goal in this monograph is to demonstrate how the minute structure of fractals is unfolded when seen in the light of related dynamics. A co-publication of the AMS and CBMS.
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.
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.
Fractals In Probability And Analysis
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Author : Christopher J. Bishop
language : en
Publisher: Cambridge University Press
Release Date : 2017
Fractals In Probability And Analysis written by Christopher J. Bishop and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Mathematics categories.
A mathematically rigorous introduction to fractals, emphasizing examples and fundamental ideas while minimizing technicalities.
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.