Fractal geometry Books
Oxford University Press Chaos and Fractals
Book SynopsisThis book provides the reader with an elementary introduction to chaos and fractals, suitable for students with a background in elementary algebra, without assuming prior coursework in calculus or physics. It introduces the key phenomena of chaos - aperiodicity, sensitive dependence on initial conditions, bifurcations - via simple iterated functions. Fractals are introduced as self-similar geometric objects and analyzed with the self-similarity and box-counting dimensions. After a brief discussion of power laws, subsequent chapters explore Julia Sets and the Mandelbrot Set. The last part of the book examines two-dimensional dynamical systems, strange attractors, cellular automata, and chaotic differential equations.The book is richly illustrated and includes over 200 end-of-chapter exercises. A flexible format and a clear and succinct writing style make it a good choice for introductory courses in chaos and fractals.Trade Review... obtains top marks ... For any lecturer or teacher looking for a text on these subjects, this book is worthy of your consideration. * Gazette of the Australian Mathematical Society *For the right audience and instructor, this is a wonderful book. With considerable effort on both sides it can take a wide audience with modest mathematics to a reasonable understanding of what is behind much of the complex phenomena seen in modern mathematical models of the physical universe. * Thomas B. Ward, Zentralblatt MATH *This is an excellent book, and is highly recommended. * Mark Hunacek, Mathematical Association of America *The only textbook on chaos and fractals for non-science and mathematics majors. Covers central phenomena and ideas of chaos and fractals in a careful, intellectually honest, but accessible way. * L'Enseignement Mathematique (2) 59 *Chaos and fractals are two intertwined concepts that have revolutionized many areas of science and renewed popular interest in mathematics over the past few decades. Feldman's book is a rich resource for anyone who wants a deeper understanding of these subjects without the need for advanced mathematics. * Julien Clinton Sprott, University of Wisconsin-Madison *The style of writing is easy on the reader. The explanations are clear and illustrated with many diagrams and side notes....[Feldman] has produced an excellent book. * John Sykes, Mathematics in School *David P. Feldman provides a delightful and thoughtful introduction to chaos and fractals requiring only a good background in algebra. The formal treatment of nonlinear dynamics, chaotic behavior, Lyapunov exponents, and fractal dimensions is leavened with creative analogies and many helpful and visually attractive figures and diagrams. Even more mathematically sophisticated readers will find this book a good starting point in exploring the complex and beguiling realms of chaos and fractals. * Robert C. Hilborn, Associate Executive Officer, American Association of Physics Teachers *For the right audience and instructor, this is a wonderful book. With considerable effort on both sides it can take a wide audience with modest mathematics to a reasonable understanding of what is behind much of the complex phenomena seen in modern mathematical models of the physical universe. * Thomas B. Ward, Durham University *The book is very well produced, with excellent diagrams and very informative notes provided beside the main text. It also provides an extensive list of references for further reading. * Scottish Mathematical Council Journal *[haos and Fractals] offers at least the possibility of a radically different trajectory for school teaching, providing a motivated pathway to a lot of fascinating mathematics not normally considered accessible ... * Danny Yee, Danny Reviews *Table of ContentsI. INTRODUCING DISCRETE DYNAMICAL SYSTEMS; II. CHAOS; III. FRACTALS; IV. JULIA SETS AND THE MANDELBROT SET; V. HIGHER-DIMENSIONAL SYSTEMS; VI. CONCLUSION; VII. APPENDICES
£40.84
Oxford University Press Fractals
Book SynopsisMany are familiar with the beauty and ubiquity of fractal forms within nature. Unlike the study of smooth forms such as spheres, fractal geometry describes more familiar shapes and patterns, such as the complex contours of coastlines, the outlines of clouds, and the branching of trees. In this Very Short Introduction, Kenneth Falconer looks at the roots of the ''fractal revolution'' that occurred in mathematics in the 20th century, presents the ''new geometry'' of fractals, explains the basic concepts, and explores the wide range of applications in science, and in aspects of economics.This is essential introductory reading for students of mathematics and science, and those interested in popular science and mathematics.ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.Trade ReviewFractals: A Very Short Introduction is an obvious starting point for lay readers interested in fractals. It presents the key ideas and explains their context and significance, while introducing and using some very basic mathematics. * Danny Yee's Book Reviews *a most enjoyable, 'short read' * Institute of Mathematics *[A] very well-written introduction to fractals for non-specialists ... Highly recommended. * CHOICE *Table of ContentsPreface ; 1. The fractal concept ; 2. Self-similarity ; 3. Fractal dimension ; 4. Julia sets and the Mandelbrot set ; 5. Random walks and Brownian motion ; 6. Fractals in the real world ; 7. A little history ; Further reading
£9.49
John Wiley & Sons Inc Fractal Geometry
Book SynopsisThis comprehensive and popular textbook makes fractal geometry accessible to final-year undergraduate math or physics majors, while also serving as a reference for research mathematicians or scientists. This up-to-date edition covers introductory multifractal theory, random fractals, and modern applications in finance and science.Trade Review“Falconer’s book is excellent in many respects and the reviewer strongly recommends it. May every university library own a copy, or three! And if you’re a student reading this, go check it out today!.” (Mathematical Association of America, 11 June 2014)Table of ContentsPreface to the first edition ix Preface to the second edition xiii Preface to the third edition xv Course suggestions xvii Introduction xix PART I FOUNDATIONS 1 1 Mathematical background 3 1.1 Basic set theory 3 1.2 Functions and limits 7 1.3 Measures and mass distributions 11 1.4 Notes on probability theory 17 1.5 Notes and references 24 Exercises 24 2 Box-counting dimension 27 2.1 Box-counting dimensions 27 2.2 Properties and problems of box-counting dimension 34 *2.3 Modified box-counting dimensions 38 2.4 Some other definitions of dimension 40 2.5 Notes and references 41 Exercises 42 3 Hausdorff and packing measures and dimensions 44 3.1 Hausdorff measure 44 3.2 Hausdorff dimension 47 3.3 Calculation of Hausdorff dimension – simple examples 51 3.4 Equivalent definitions of Hausdorff dimension 53 *3.5 Packing measure and dimensions 54 *3.6 Finer definitions of dimension 57 *3.7 Dimension prints 58 *3.8 Porosity 60 3.9 Notes and references 63 Exercises 64 4 Techniques for calculating dimensions 66 4.1 Basic methods 66 4.2 Subsets of finite measure 75 4.3 Potential theoretic methods 77 *4.4 Fourier transform methods 80 4.5 Notes and references 81 Exercises 81 5 Local structure of fractals 83 5.1 Densities 84 5.2 Structure of 1-sets 87 5.3 Tangents to s-sets 92 5.4 Notes and references 96 Exercises 96 6 Projections of fractals 98 6.1 Projections of arbitrary sets 98 6.2 Projections of s-sets of integral dimension 101 6.3 Projections of arbitrary sets of integral dimension 103 6.4 Notes and references 105 Exercises 106 7 Products of fractals 108 7.1 Product formulae 108 7.2 Notes and references 116 Exercises 116 8 Intersections of fractals 118 8.1 Intersection formulae for fractals 119 *8.2 Sets with large intersection 122 8.3 Notes and references 128 Exercises 128 PART II APPLICATIONS AND EXAMPLES 131 9 Iterated function systems – self-similar and self-affine sets 133 9.1 Iterated function systems 133 9.2 Dimensions of self-similar sets 139 CONTENTS vii 9.3 Some variations 143 9.4 Self-affine sets 149 9.5 Applications to encoding images 155 *9.6 Zeta functions and complex dimensions 158 9.7 Notes and references 167 Exercises 167 10 Examples from number theory 169 10.1 Distribution of digits of numbers 169 10.2 Continued fractions 171 10.3 Diophantine approximation 172 10.4 Notes and references 176 Exercises 176 11 Graphs of functions 178 11.1 Dimensions of graphs 178 *11.2 Autocorrelation of fractal functions 188 11.3 Notes and references 192 Exercises 192 12 Examples from pure mathematics 195 12.1 Duality and the Kakeya problem 195 12.2 Vitushkin’s conjecture 198 12.3 Convex functions 200 12.4 Fractal groups and rings 201 12.5 Notes and references 204 Exercises 204 13 Dynamical systems 206 13.1 Repellers and iterated function systems 208 13.2 The logistic map 209 13.3 Stretching and folding transformations 213 13.4 The solenoid 217 13.5 Continuous dynamical systems 220 *13.6 Small divisor theory 225 *13.7 Lyapunov exponents and entropies 228 13.8 Notes and references 231 Exercises 232 14 Iteration of complex functions – Julia sets and the Mandelbrot set 235 14.1 General theory of Julia sets 235 14.2 Quadratic functions – the Mandelbrot set 243 14.3 Julia sets of quadratic functions 248 14.4 Characterisation of quasi-circles by dimension 256 14.5 Newton’s method for solving polynomial equations 258 14.6 Notes and references 262 Exercises 262 15 Random fractals 265 15.1 A random Cantor set 266 15.2 Fractal percolation 272 15.3 Notes and references 277 Exercises 277 16 Brownian motion and Brownian surfaces 279 16.1 Brownian motion in ℝ 279 16.2 Brownian motion in ℝn 285 16.3 Fractional Brownian motion 289 16.4 Fractional Brownian surfaces 294 16.5 Lévy stable processes 296 16.6 Notes and references 299 Exercises 299 17 Multifractal measures 301 17.1 Coarse multifractal analysis 302 17.2 Fine multifractal analysis 307 17.3 Self-similar multifractals 310 17.4 Notes and references 320 Exercises 320 18 Physical applications 323 18.1 Fractal fingering 325 18.2 Singularities of electrostatic and gravitational potentials 330 18.3 Fluid dynamics and turbulence 332 18.4 Fractal antennas 334 18.5 Fractals in finance 336 18.6 Notes and references 340 Exercises 341 References 342 Index 357
£40.80
Nova Science Publishers Inc Fractals & Local Order in Polymeric Materials
Book SynopsisFractals & Local Order in Polymeric Materials
£113.59
Nova Science Publishers Inc Fractals, Applied Synergetics & Structure Design
Book SynopsisNon-linear systems behaviours are discussed in this book from the point of new scientific approaches to the interdiscipline nature of the fractal geometry and synergetics. Fractal analysis, synergetics methods and mathematical design are considered according to actual problems of condensed media physics, mechanics, material science and geology.
£143.24
Nova Science Publishers Inc Handbook on the Classification & Application of
Book Synopsis
£146.24
Icon Books Introducing Fractals: A Graphic Guide
Book SynopsisFractals are the geometry of the natural world. They're about the broken, wrinkled, wiggly world- the uneven shapes of nature, unlike the idealised forms of Euclidean geometry. We see fractals everywhere; indeed, we are fractals ourselves. Fractal geometry is an extension of classical geometry which can make precise models of physical structures, from ferns to galaxies. It can describe the shape of a cloud as precisely as an architect can describe a house. Introducing Fractals traces the historical development of this mathematical discipline, explores its descriptive powers in the natural world, and then looks at the applications and the implications of the discoveries it has made. As John Archibald Wheeler, protégé of Niels Bohr, friend of Albert Einstein and mentor of Richard Feynman has said, 'No one will be considered scientifically literate tomorrow, who is not familiar with fractals.'
£8.54
World Scientific Publishing Co Pte Ltd Fractal Growth Phenomena (2nd Edition)
Book SynopsisThe investigation of phenomena involving fractals has gone through a spectacular development in the last decade. Many physical, technological and biological processes have been shown to be related to and described by objects with non-integer dimensions. The physics of far-from-equilibrium growth phenomena represents one of the most important fields in which fractal geometry is widely applied. During the last couple of years considerable experimental, numerical and theoretical information has accumulated concerning such processes.This book, written by a well-known expert in the field, summarizes the basic concepts born in the studies of fractal growth and also presents some of the most important new results for more specialized readers. It also contains 15 beautiful color plates demonstrating the richness of the geometry of fractal patterns. Accordingly, it may serve as a textbook on the geometrical aspects of fractal growth and it treats this area in sufficient depth to make it useful as a reference book. No specific mathematical knowledge is required for reading this book which is intended to give a balanced account of the field.Trade Review"The book 'Fractal Growth Phenomena' by T Vicsek is a complete up-to-date introduction, documentation and reference guide to this field. The book is written in a precise and fascinating manner. The clear style allows a fast understanding of the material also for those who did not study mathematics or physics." Martin Obert Justus-Liebig-Universitat Giessen "In summary the book offers an excellent introduction to and overview of a rapidly expanding field. It will serve as both a standard reference work for those already working in the area and as a comprehensive introduction for those wishing to learn more." Murray T Batchelor Australian & New Zealand Physicist, 1995Table of ContentsForeword, B. Mandelbrot; introduction; fractal geometry; fractal measures; methods for determining fractal dimensions; local growth models; diffusion-limited growth; growing self-affine surfaces; cluster-cluster aggregation (CCA); computer simulations; experiments on Laplacian growth; new developments.
£103.50
World Scientific Publishing Co Pte Ltd Fractal Growth Phenomena (2nd Edition)
Book SynopsisThe investigation of phenomena involving fractals has gone through a spectacular development in the last decade. Many physical, technological and biological processes have been shown to be related to and described by objects with non-integer dimensions. The physics of far-from-equilibrium growth phenomena represents one of the most important fields in which fractal geometry is widely applied. During the last couple of years considerable experimental, numerical and theoretical information has accumulated concerning such processes.This book, written by a well-known expert in the field, summarizes the basic concepts born in the studies of fractal growth and also presents some of the most important new results for more specialized readers. It also contains 15 beautiful color plates demonstrating the richness of the geometry of fractal patterns. Accordingly, it may serve as a textbook on the geometrical aspects of fractal growth and it treats this area in sufficient depth to make it useful as a reference book. No specific mathematical knowledge is required for reading this book which is intended to give a balanced account of the field.Trade Review"The book 'Fractal Growth Phenomena' by T Vicsek is a complete up-to-date introduction, documentation and reference guide to this field. The book is written in a precise and fascinating manner. The clear style allows a fast understanding of the material also for those who did not study mathematics or physics." Martin Obert Justus-Liebig-Universitat Giessen "In summary the book offers an excellent introduction to and overview of a rapidly expanding field. It will serve as both a standard reference work for those already working in the area and as a comprehensive introduction for those wishing to learn more." Murray T Batchelor Australian & New Zealand Physicist, 1995Table of ContentsForeword, B. Mandelbrot; introduction; fractal geometry; fractal measures; methods for determining fractal dimensions; local growth models; diffusion-limited growth; growing self-affine surfaces; cluster-cluster aggregation (CCA); computer simulations; experiments on Laplacian growth; new developments.
£59.85
World Scientific Publishing Co Pte Ltd Fractal Space-time And Microphysics: Towards A
Book SynopsisThis is the first detailed account of a new approach to microphysics based on two leading ideas: (i) the explicit dependence of physical laws on scale encountered in quantum physics, is the manifestation of a fundamental principle of nature, scale relativity. This generalizes Einstein's principle of (motion) relativity to scale transformations; (ii) the mathematical achievement of this principle needs the introduction of a nondifferentiable space-time varying with resolution, i.e. characterized by its fractal properties.The author discusses in detail reactualization of the principle of relativity and its application to scale transformations, physical laws which are explicitly scale dependent, and fractals as a new geometric description of space-time.Table of ContentsGeneral introduction; from fractal objects to fractal spaces; fractal dimension of a quantum path; the fractal structure of the quantum space-time; towards a linear theory of scale relativity; prospects.
£77.90
World Scientific Publishing Co Pte Ltd Fractals In Natural Science
Book SynopsisDuring the last couple of years, fractals have been shown to represent the common aspects of many complex processes occurring in an unusually diverse range of fields including biology, chemistry, earth sciences, physics and technology. Using fractal geometry as a language, it has become possible to get a deeper insight into previously intractable problems. Among many others, a better understanding of growth phenomena, turbulence, iteractive functions, colloidal aggregation, biological pattern formation and inhomogenous materials has emerged through the application of such concepts as scale invariance, self-affinity and multifractality.This volume contains a selection of high quality papers that discuss the latest developments in the research of fractals. It is divided into 5 sections and contains altogether 64 papers. Each paper is written by a well known author or authors in the field. Beginning each section is a short introduction, written by a prominent author, which gives a brief overview of the topics discussed in the respective sections.Table of ContentsPower Law Distribution of River Basin Sizes (H Takayasu); The Fixed Scale Transformation: Status and Perspective (L Pietronereo); Structures Generated by Model Nonlinear Hamiltonians Based on Ocean Waves (J Willemsen); Self-Similar Colony Morphogenesis by Bacteria as the Experimental Model of Fractal Growth by a Cell Population (T Matsuyama et al); Vibrational Problem of Fractal Networks (T Nakayama); Fractal Tectonics and Erosion (D L Turcotte); Examples of Fractals in Soil Mechanics (H J Herrmann et al); Granular Cocktail Rotated and Shaken (G Baumann et al); Critical Exponents of Elasticity in a Continuum Percolation System (K Maruyama et al); Statistics of Fracture Surfaces (J Planes et al); Fractal Analyses of Anisotropic Fracture Surfaces (B L Cox & J S Y Wang); Effect of High Magnetic Fields on Fractal Growth of Silver Metal-Forest (S Okubo et al).
£119.70
World Scientific Publishing Co Pte Ltd Fractals In Reservoir Engineering
Book SynopsisMany natural objects have been found to be fractal and fractal mathematics has been used to generate many beautiful “nature” scenes. Fractal mathematics is used in image compression and for movies and is now becoming an engineering tool as well. This book describes the application of fractal mathematics to one engineering specialty — reservoir engineering. This is the process of engineering the production of oil and gas. The reservoir engineer's job is to design and predict production from underground oil and gas reservoirs. The successful application of fractal mathematics to this engineering discipline should be of interest, not only to reservoir engineers, but to other engineers with their own potential applications as well. Geologists will find surprisingly good numerical descriptions of subsurface rock distributions. Physicists will be interested in the application of renormalization and percolation theory described in the book. Geophysicists will find the description of fluid flow scaling problems faced by the reservoir engineer similar to their problems of scaling the transport of acoustic signals.
£59.85
World Scientific Publishing Co Pte Ltd Exotic Smoothness And Physics: Differential
Book SynopsisThe recent revolution in differential topology related to the discovery of non-standard (”exotic”) smoothness structures on topologically trivial manifolds such as R4 suggests many exciting opportunities for applications of potentially deep importance for the spacetime models of theoretical physics, especially general relativity. This rich panoply of new differentiable structures lies in the previously unexplored region between topology and geometry. Just as physical geometry was thought to be trivial before Einstein, physicists have continued to work under the tacit — but now shown to be incorrect — assumption that differentiability is uniquely determined by topology for simple four-manifolds. Since diffeomorphisms are the mathematical models for physical coordinate transformations, Einstein's relativity principle requires that these models be physically inequivalent. This book provides an introductory survey of some of the relevant mathematics and presents preliminary results and suggestions for further applications to spacetime models.Trade Review"... the authors have made a great effort to give enough details (being careful with definitions and with statements of theorems) so that the reader can get something more than the mere flavor of the subject ... References for all results are given throughout the book, and this may induce the interested reader to go more deeply into the subject."Mathematical Reviews"Readers who are willing to take this possibility into account will find this book most stimulating. I recommended it to everyone interested in the fundamentals of spacetime theory."General Relativity and GravitationTable of ContentsIntroduction and Background; Algebraic Tools for Topology; Smooth Manifolds, Geometry; Bundles, Geometry, Gauge Theory; Gauge Theory and Moduli Space; A Guide to the Classification of Manifolds; Early Exotic Manifolds; The First Results in Dimension Four; Seiberg-Witten Theory: The Modern Approach; Physical Implications; From Differential Structures to Operator Algebras and Geometric Structures.
£104.40
World Scientific Publishing Co Pte Ltd Analysis, Probability And Mathematical Physics On
Book SynopsisIn the 50 years since Mandelbrot identified the fractality of coastlines, mathematicians and physicists have developed a rich and beautiful theory describing the interplay between analytic, geometric and probabilistic aspects of the mathematics of fractals. Using classical and abstract analytic tools developed by Cantor, Hausdorff, and Sierpinski, they have sought to address fundamental questions: How can we measure the size of a fractal set? How do waves and heat travel on irregular structures? How are analysis, geometry and stochastic processes related in the absence of Euclidean smooth structure? What new physical phenomena arise in the fractal-like settings that are ubiquitous in nature?This book introduces background and recent progress on these problems, from both established leaders in the field and early career researchers. The book gives a broad introduction to several foundational techniques in fractal mathematics, while also introducing some specific new and significant results of interest to experts, such as that waves have infinite propagation speed on fractals. It contains sufficient introductory material that it can be read by new researchers or researchers from other areas who want to learn about fractal methods and results.
£130.50
World Scientific Publishing Co Pte Ltd Kitchen Science Fractals: A Lab Manual For
Book SynopsisThis book provides a collection of 44 simple computer and physical laboratory experiments, including some for an artist's studio and some for a kitchen, that illustrate the concepts of fractal geometry. In addition to standard topics — iterated function systems (IFS), fractal dimension computation, the Mandelbrot set — we explore data analysis by driven IFS, construction of four-dimensional fractals, basic multifractals, synchronization of chaotic processes, fractal finger paints, cooking fractals, videofeedback, and fractal networks of resistors and oscillators.
£112.50
World Scientific Publishing Co Pte Ltd Kitchen Science Fractals: A Lab Manual For
Book SynopsisThis book provides a collection of 44 simple computer and physical laboratory experiments, including some for an artist's studio and some for a kitchen, that illustrate the concepts of fractal geometry. In addition to standard topics — iterated function systems (IFS), fractal dimension computation, the Mandelbrot set — we explore data analysis by driven IFS, construction of four-dimensional fractals, basic multifractals, synchronization of chaotic processes, fractal finger paints, cooking fractals, videofeedback, and fractal networks of resistors and oscillators.
£42.75
World Scientific Publishing Co Pte Ltd Lectures On Fractal Geometry
Book SynopsisThis book is based on a series of lectures at the Mathematics Department of the University of Jena, developed in the period from 1995 up to 2015. It is completed by additional material and extensions of some basic results from the literature to more general metric spaces.This book provides a clear introduction to classical fields of fractal geometry, which provide some background for modern topics of research and applications. Some basic knowledge on general measure theory and on topological notions in metric spaces is presumed.
£66.50
World Scientific Publishing Co Pte Ltd Fractalize That! : A Visual Essay On Statistical
Book SynopsisFractalize That! A Visual Essay on Statistical Geometry brings a new class of geometric fractals to a wider audience of mathematicians and scientists. It describes a recently discovered random fractal space-filling algorithm. Connections with tessellations and known fractals such as Sierpinski are developed. And, the mathematical development is illustrated by a large number of colorful images that will charm the readers.The algorithm claims to be universal in scope, in that it can fill any spatial region with smaller and smaller fill regions of any shape. The filling is complete in the limit of an infinite number of fill regions. This book presents a descriptive development of the subject using the traditional shapes of geometry such as discs, squares, and triangles. It contains a detailed mathematical treatment of all that is currently known about the algorithm, as well as a chapter on software implementation of the algorithm.The mathematician will find a wealth of interesting conjectures supported by numerical computation. Physicists are offered a model looking for an application. The patterns generated are often quite interesting as abstract art. Readers can also create these computer-generated art with the advice and examples provided.
£66.50
World Scientific Publishing Co Pte Ltd Fractional Order Systems: Modeling And Control
Book SynopsisThis book aims to propose the implementation and application of Fractional Order Systems (FOS). It is well known that FOS can be utilized in control applications and systems modeling, and their effectiveness has been proven in many theoretical works and simulation routines. A further and mandatory step for FOS real world utilization is their hardware implementation and applications on real systems modeling. With this viewpoint, introductory chapters are included on the definition of stability region of Fractional Order PID Controller and Chaotic FOS, followed by the practical implementation based on Microcontroller, Field Programmable Gate Array, Field Programmable Analog Array and Switched Capacitor. Another section is dedicated to FO modeling of Ionic Polymeric Metal Composite (IPMC). This new material will have applications in robotics, aerospace and biomedicine.Table of ContentsFractional Order Systems; Fractional Order PID Controller; Chaotic Fractional Order Systems; Field Programmable Gate Array, Microcontroller and Field Programmable Analog Array Implementation; Switched Capacitor and Integrated Circuit Design; Modeling of Ionic Polymeric Metal Composite;
£82.65
