Mathematics

Introducing Fractal Geometry

Author: Nigel Lesmoir-Gordon,Will Rood,Ralph Edney

Publisher: Totem Books

ISBN: 9781840467130

Category: Mathematics

Page: 174

View: 8735

Fractal geometry is the geometry of the natural world. It mirrors the uneven but real shapes of nature, the world as we actually experience it. Introducing Fractal Geometry traces the development of this revolutionary new discipline.
Mathematics

Introducing Fractals

A Graphic Guide

Author: Nigel Lesmoir-Gordon,Will Rood

Publisher: Icon Books Ltd

ISBN: 1848317832

Category: Mathematics

Page: 176

View: 3228

From Zeno to Mandelbrot: explore this new language with which you can describe the shape of cloud as precisely as an architect can describe a house.
Mathematics

Introducing Fractals

A Graphic Guide

Author: Nigel Lesmoir-Gordon,Will Rood

Publisher: Icon Books Ltd

ISBN: 1848317832

Category: Mathematics

Page: 176

View: 1213

From Zeno to Mandelbrot: explore this new language with which you can describe the shape of cloud as precisely as an architect can describe a house.
Mathematics

Fractals: A Very Short Introduction

Author: K. J. Falconer

Publisher: Oxford University Press

ISBN: 0199675988

Category: Mathematics

Page: 132

View: 7099

An essential discussion of the popular science and mathematics behind fractals reveals how fractal shapes can be found everywhere in nature from clouds to coastlines, explaining how basic concepts in fractal geometry produced a revolution in mathematical understandings of patterns in the 20th century. Original.
Mathematics

Measure, Topology, and Fractal Geometry

Author: Gerald Edgar

Publisher: Springer Science & Business Media

ISBN: 0387747494

Category: Mathematics

Page: 272

View: 3865

Based on a course given to talented high-school students at Ohio University in 1988, this book is essentially an advanced undergraduate textbook about the mathematics of fractal geometry. It nicely bridges the gap between traditional books on topology/analysis and more specialized treatises on fractal geometry. The book treats such topics as metric spaces, measure theory, dimension theory, and even some algebraic topology. It takes into account developments in the subject matter since 1990. Sections are clear and focused. The book contains plenty of examples, exercises, and good illustrations of fractals, including 16 color plates.
Mathematics

Fractal Geometry

Mathematical Foundations and Applications

Author: Kenneth Falconer

Publisher: John Wiley & Sons

ISBN: 111876286X

Category: Mathematics

Page: 400

View: 3887

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 http://www.wileyeurope.com/fractal Leads onto the more advanced sequel Techniques in Fractal Geometry (also by Kenneth Falconer and available from Wiley)
Design

Alt.fractals

A Visual Guide to Fractal Geometry and Design

Author: Eric Baird

Publisher: Chocolate Tree Books

ISBN: 0955706831

Category: Design

Page: 232

View: 1624

A range of fractal types and variations drawn and discussed, with over 200 illustrations and diagrams.
Juvenile Nonfiction

The Fractal Geometry of Nature

Author: Benoit B. Mandelbrot

Publisher: Macmillan

ISBN: 9780716711865

Category: Juvenile Nonfiction

Page: 468

View: 3490

Three classic fractals, tamed. Galaxies and eddies. Scaling fractals. Nonscaling fractals. Self-mapping fractals. Randomness. Stratified random fractals. Fractional brown fractals. A book-within-the-book, in color. Random tremas; texture. Miscellany. Of men and ideas.
Mathematics

Fractal Geometry

Mathematical Foundations and Applications

Author: Kenneth Falconer

Publisher: John Wiley & Sons

ISBN: 0470299452

Category: Mathematics

Page: 366

View: 2601

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 Please click here to download solutions to exercises found within this title: http://www.wileyeurope.com/fractal
Mathematics

The Geometry of Fractal Sets

Author: K. J. Falconer

Publisher: Cambridge University Press

ISBN: 9780521337052

Category: Mathematics

Page: 162

View: 885

This book contains a rigorous mathematical treatment of the geometrical aspects of sets of both integral and fractional Hausdorff dimension. Questions of local density and the existence of tangents of such sets are studied, as well as the dimensional properties of their projections in various directions. In the case of sets of integral dimension the dramatic differences between regular 'curve-like' sets and irregular 'dust like' sets are exhibited. The theory is related by duality to Kayeka sets (sets of zero area containing lines in every direction). The final chapter includes diverse examples of sets to which the general theory is applicable: discussions of curves of fractional dimension, self-similar sets, strange attractors, and examples from number theory, convexity and so on. There is an emphasis on the basic tools of the subject such as the Vitali covering lemma, net measures and Fourier transform methods.
Science

Fractals, Chaos, Power Laws

Minutes from an Infinite Paradise

Author: Manfred Schroeder

Publisher: Courier Corporation

ISBN: 0486472043

Category: Science

Page: 448

View: 951

This fascinating book explores the connections between chaos theory, physics, biology, and mathematics. Its award-winning computer graphics, optical illusions, and games illustrate the concept of self-similarity, a typical property of fractals. The author - hailed by Publishers Weekly as a modern Lewis Carroll - conveys memorable insights in the form of puns and puzzles. 1992 edition.
Mathematics

Fractals Everywhere

New Edition

Author: Michael F. Barnsley

Publisher: Courier Corporation

ISBN: 0486320340

Category: Mathematics

Page: 560

View: 526

Up-to-date text focuses on how fractal geometry can be used to model real objects in the physical world, with an emphasis on fractal applications. Includes solutions, hints, and a bonus CD.
Ergodic theory

Fractal Geometry and Applications: Analysis, number theory, and dynamical systems

Author: Benoit B. Mandelbrot,Michel Laurent Lapidus

Publisher: American Mathematical Soc.

ISBN: 0821836374

Category: Ergodic theory

Page: 517

View: 8605

This volume offers an excellent selection of cutting-edge articles about fractal geometry, covering the great breadth of mathematics and related areas touched by this subject. Included are rich survey articles and fine expository papers. The high-quality contributions to the volume by well-known researchers--including two articles by Mandelbrot--provide a solid cross-section of recent research representing the richness and variety of contemporary advances in and around fractal geometry. In demonstrating the vitality and diversity of the field, this book will motivate further investigation into the many open problems and inspire future research directions. It is suitable for graduate students and researchers interested in fractal geometry and its applications. This is a two-part volume. Part 1 covers analysis, number theory, and dynamical systems; Part 2, multifractals, probability and statistical mechanics, and applications.
Mathematics

Fractal Analysis

Author: Clifford Brown,Larry Liebovitch

Publisher: SAGE

ISBN: 1412971659

Category: Mathematics

Page: 90

View: 5348

As one of the only texts introducing fractal analysis and the social processes involved to social science readers, this is a must-have book for those looking to gain an understanding of this area of analysis.
Mathematics

Fractal Geometries Theory and Applications

Author: Alain Le Mehaute

Publisher: CRC Press

ISBN: 9780849377228

Category: Mathematics

Page: 200

View: 4225

Fractal geometry, based on recursive mathematical schemas, provides a means for modeling a great number of natural phenomena. For this reason, it is of increasing interest to physicists, chemists, biologists, and geographers, among others. A major quality of fractality is that it not only unifies phenomena previously thought to be anomalous or disparate in a single theoretical framework, but it also promotes a return to graphical treatment, which had been almost completely banished from scientific thought in favor of analysis. This book casts a new, lively light on scientific territories still not fully explored. It is designed for research workers, engineers, and experimentalists faced with problems of measure and action in heterogenous materials and environments. Several color plates illustrate the implications and consequences of this theory for most of the questions raised by the taking into consideration of time in a fractal space.
Mathematics

The Science of Fractal Images

Author: Heinz-Otto Peitgen,Dietmar Saupe

Publisher: Springer Science & Business Media

ISBN: 146123784X

Category: Mathematics

Page: 312

View: 5813

This book is based on notes for the course Fractals:lntroduction, Basics and Perspectives given by MichaelF. Barnsley, RobertL. Devaney, Heinz-Otto Peit gen, Dietmar Saupe and Richard F. Voss. The course was chaired by Heinz-Otto Peitgen and was part of the SIGGRAPH '87 (Anaheim, California) course pro gram. Though the five chapters of this book have emerged from those courses we have tried to make this book a coherent and uniformly styled presentation as much as possible. It is the first book which discusses fractals solely from the point of view of computer graphics. Though fundamental concepts and algo rithms are not introduced and discussed in mathematical rigor we have made a serious attempt to justify and motivate wherever it appeared to be desirable. Ba sic algorithms are typically presented in pseudo-code or a description so close to code that a reader who is familiar with elementary computer graphics should find no problem to get started. Mandelbrot's fractal geometry provides both a description and a mathemat ical model for many of the seemingly complex forms and patterns in nature and the sciences. Fractals have blossomed enormously in the past few years and have helped reconnect pure mathematics research with both natural sciences and computing. Computer graphics has played an essential role both in its de velopment and rapidly growing popularity. Conversely, fractal geometry now plays an important role in the rendering, modelling and animation of natural phenomena and fantastic shapes in computer graphics.
Mathematics

Some Novel Types of Fractal Geometry

Author: Stephen Semmes

Publisher: Oxford University Press

ISBN: 9780198508069

Category: Mathematics

Page: 164

View: 5834

The present book deals with fractal geometries which have features similar to ones of ordinary Euclidean spaces, while at the same time being quite different from Euclidean spaces in other ways. A basic type of feature being considered is the presence of Sobolev or Poincare inequalities, concerning the relationship between the average behaviour of a function and the average behaviour of its small-scale oscillations. Remarkable results in the last few years of Bourdon-Pajot and Laakso haveshown that there is much more in the way of geometries like this than has been realized. Examples related to nilpotent Lie groups and Carnot metrics were known previously. On the other hand, 'typical' fractals that might be seen in pictures do not have these same kinds of features. 'Some Novel Types of Fractal Geometry' will be of interest to graduate students and researchers in mathematics, working in various aspects of geometry and analysis.
Mathematics

Computers, Rigidity, and Moduli

The Large-scale Fractal Geometry of Riemannian Moduli Space

Author: Shmuel Bochner,Shmuel Weinberger

Publisher: Princeton University Press

ISBN: 9780691118895

Category: Mathematics

Page: 174

View: 6663

This book is the first to present a new area of mathematical research that combines topology, geometry, and logic. Shmuel Weinberger seeks to explain and illustrate the implications of the general principle, first emphasized by Alex Nabutovsky, that logical complexity engenders geometric complexity. He provides applications to the problem of closed geodesics, the theory of submanifolds, and the structure of the moduli space of isometry classes of Riemannian metrics with curvature bounds on a given manifold. Ultimately, geometric complexity of a moduli space forces functions defined on that space to have many critical points, and new results about the existence of extrema or equilibria follow. The main sort of algorithmic problem that arises is recognition: is the presented object equivalent to some standard one? If it is difficult to determine whether the problem is solvable, then the original object has doppelgängers--that is, other objects that are extremely difficult to distinguish from it. Many new questions emerge about the algorithmic nature of known geometric theorems, about "dichotomy problems," and about the metric entropy of moduli space. Weinberger studies them using tools from group theory, computability, differential geometry, and topology, all of which he explains before use. Since several examples are worked out, the overarching principles are set in a clear relief that goes beyond the details of any one problem.
Mathematics

Fractals

Endlessly Repeated Geometrical Figures

Author: Hendrik Adolf Lauwerier

Publisher: N.A

ISBN: 9780691024455

Category: Mathematics

Page: 209

View: 7896

Fractals are shapes in which an identical motif repeats itself on an ever diminishing scale. A coastline, for instance, is a fractal, with each bay or headland having its own smaller bays and headlands--as is a tree with a trunk that separates into two smaller side branches, which in their turn separate into side branches that are smaller still. No longer mathematical curiosities, fractals are now a vital subject of mathematical study, practical application, and popular interest. For readers interested in graphic design, computers, and science and mathematics in general, Hans Lauwerier provides an accessible introduction to fractals that makes only modest use of mathematical techniques. Lauwerier calls this volume a "book to work with." Readers with access to microcomputers can design new figures, as well as re-create famous examples. They can start with the final chapter, try out one of the programs described there (preferably in a compiled version such as TURBO BASIC), and consult the earlier chapters for whatever is needed to understand the fractals produced in this way. The first chapter, which builds on the relationship of binary number systems to the "tree fractal" described above, is the best place to start if one has no computer. There will be much to enjoy on the way, including the beautiful color illustrations.
Mathematics

Chaotic Dynamics and Fractals

Author: Michael F. Barnsley,Stephen G. Demko

Publisher: Academic Press

ISBN: 1483269086

Category: Mathematics

Page: 304

View: 7531

Chaotic Dynamics and Fractals covers the proceedings of the 1985 Conference on Chaotic Dynamics, held at the Georgia Institute of Technology. This conference deals with the research area of chaos, dynamical systems, and fractal geometry. This text is organized into three parts encompassing 16 chapters. The first part describes the nature of chaos and fractals, the geometric tool for some strange attractors, and other complicated sets of data associated with chaotic systems. This part also considers the Henon-Hiles Hamiltonian with complex time, a Henon family of maps from C2 into itself, and the idea of turbulent maps in the course of presenting results on iteration of continuous maps from the unit interval to itself. The second part discusses complex analytic dynamics and associated fractal geometry, specifically the bursts into chaos, algorithms for obtaining geometrical and combinatorial information, and the parameter space for iterated cubic polynomials. This part also examines the differentiation of Julia sets with respects to a parameter in the associated rational map, permitting the formulation of Taylor series expansion for the sets. The third part highlights the applications of chaotic dynamics and fractals. This book will prove useful to mathematicians, physicists, and other scientists working in, or introducing themselves to, the field.