# Search Results for "introducing-fractal-geometry"

## Introducing Fractal Geometry

**Author**: Nigel Lesmoir-Gordon,Will Rood,Ralph Edney**Publisher:**Totem Books**ISBN:**9781840467130**Category:**Mathematics**Page:**174**View:**9546

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.

## Introducing Fractals

*A Graphic Guide*

**Author**: Nigel Lesmoir-Gordon,Will Rood**Publisher:**Icon Books Ltd**ISBN:**1848317832**Category:**Mathematics**Page:**176**View:**7393

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.

## Introducing Fractals

*A Graphic Guide*

**Author**: Nigel Lesmoir-Gordon,Will Rood**Publisher:**Icon Books Ltd**ISBN:**1848317832**Category:**Mathematics**Page:**176**View:**4772

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.

## The Fractal Geometry of Nature

**Author**: Benoit B. Mandelbrot**Publisher:**Macmillan**ISBN:**9780716711865**Category:**Juvenile Nonfiction**Page:**468**View:**6323

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.

## Fractals: A Very Short Introduction

**Author**: K. J. Falconer**Publisher:**Oxford University Press**ISBN:**0199675988**Category:**Mathematics**Page:**132**View:**924

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.

## Measure, Topology, and Fractal Geometry

**Author**: Gerald Edgar**Publisher:**Springer Science & Business Media**ISBN:**0387747494**Category:**Mathematics**Page:**272**View:**7738

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.

## Fractal Geometry

*Mathematical Foundations and Applications*

**Author**: Kenneth Falconer**Publisher:**John Wiley & Sons**ISBN:**0470299452**Category:**Mathematics**Page:**366**View:**5607

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

## Alt.fractals

*A Visual Guide to Fractal Geometry and Design*

**Author**: Eric Baird**Publisher:**Chocolate Tree Books**ISBN:**0955706831**Category:**Design**Page:**232**View:**6718

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

## 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:**6737

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.

## The Geometry of Fractal Sets

**Author**: K. J. Falconer**Publisher:**Cambridge University Press**ISBN:**9780521337052**Category:**Mathematics**Page:**162**View:**7543

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.

## Fractals Everywhere

*New Edition*

**Author**: Michael F. Barnsley**Publisher:**Courier Corporation**ISBN:**0486320340**Category:**Mathematics**Page:**560**View:**4868

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.

## Fractals, Chaos, Power Laws

*Minutes from an Infinite Paradise*

**Author**: Manfred Schroeder**Publisher:**Courier Corporation**ISBN:**0486472043**Category:**Science**Page:**448**View:**6881

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.

## The Colours of Infinity

*The Beauty and Power of Fractals*

**Author**: Nigel Lesmoir-Gordon**Publisher:**Springer Science & Business Media**ISBN:**9781849964869**Category:**Mathematics**Page:**207**View:**2417

A geometry able to include mountains and clouds now exists. I put it together in 1975, but of course it incorporates numerous pieces that have been around for a very long time. Like everything in science, this new geometry has very, very deep and long roots. Benoît B. Mandelbrot Introduction This enhanced and expanded edition of THE COLOURS OF INFINITY features an additional chapter on the money markets by the fractal master himself, Professor Benoît Mandelbrot. The DVD of the film associated with this book has been re-mastered especially for this edition with exquisite new fractal animations, which will take your breath away! Driven by the curious enthusiasm that engulfs many fractalistas, in 1994, Nigel Lesmoir-Gordon overcame enormous obstacles to raise the finance for, then shoot and edit the groundbreaking TV documentary from which this book takes its name. The film has been transmitted on TV channels in over fifty countries around the world. This book is not just a celebration of the discovery of the Mandelbrot set, it also brings fractal geometry up to date with a gathering of the thoughts and enthusiasms of the foremost writers and researchers in the field. As Ian Stewart makes clear in the opening chapter, there were antecedents for fractal geometry before 1975 when Mandelbrot gave the subject its name and began to develop the underlying theory.

## Chaotic Dynamics and Fractals

**Author**: Michael F. Barnsley,Stephen G. Demko**Publisher:**Academic Press**ISBN:**1483269086**Category:**Mathematics**Page:**304**View:**2952

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.

## Chaos and Fractals

*New Frontiers of Science*

**Author**: Heinz-Otto Peitgen,Hartmut Jürgens,Dietmar Saupe**Publisher:**Springer Science & Business Media**ISBN:**1475747403**Category:**Mathematics**Page:**999**View:**8953

For almost ten years chaos and fractals have been enveloping many areas of mathematics and the natural sciences in their power, creativity and expanse. Reaching far beyond the traditional bounds of mathematics and science to the realms of popular culture, they have captured the attention and enthusiasm of a worldwide audience. The fourteen chapters of the book cover the central ideas and concepts, as well as many related topics including, the Mandelbrot Set, Julia Sets, Cellular Automata, L-Systems, Percolation and Strange Attractors, and each closes with the computer code for a central experiment. In the two appendices, Yuval Fisher discusses the details and ideas of fractal image compression, while Carl J.G. Evertsz and Benoit Mandelbrot introduce the foundations and implications of multifractals.

## Fractal Geometries Theory and Applications

**Author**: Alain Le Mehaute**Publisher:**CRC Press**ISBN:**9780849377228**Category:**Mathematics**Page:**200**View:**4298

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.

## Fractals in Probability and Analysis

**Author**: Christopher J. Bishop,Yuval Peres**Publisher:**Cambridge University Press**ISBN:**1107134110**Category:**Mathematics**Page:**412**View:**7129

This is a mathematically rigorous introduction to fractals which emphasizes examples and fundamental ideas. Building up from basic techniques of geometric measure theory and probability, central topics such as Hausdorff dimension, self-similar sets and Brownian motion are introduced, as are more specialized topics, including Kakeya sets, capacity, percolation on trees and the traveling salesman theorem. The broad range of techniques presented enables key ideas to be highlighted, without the distraction of excessive technicalities. The authors incorporate some novel proofs which are simpler than those available elsewhere. Where possible, chapters are designed to be read independently so the book can be used to teach a variety of courses, with the clear structure offering students an accessible route into the topic.

## Fractals

*Endlessly Repeated Geometrical Figures*

**Author**: Hendrik Adolf Lauwerier**Publisher:**N.A**ISBN:**9780691024455**Category:**Mathematics**Page:**209**View:**4239

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.

## Chaos and Fractals

*An Elementary Introduction*

**Author**: David P. Feldman**Publisher:**Oxford University Press**ISBN:**0199566437**Category:**Mathematics**Page:**408**View:**6707

For students with a background in elementary algebra, this book provides a vivid introduction to the key phenomena and ideas of chaos and fractals, including the butterfly effect, strange attractors, fractal dimensions, Julia Sets and the Mandelbrot Set, power laws, and cellular automata. The book includes over 200 end-of-chapter exercises.

## Handbook of Research on Visual Computing and Emerging Geometrical Design Tools

**Author**: Amoruso, Giuseppe**Publisher:**IGI Global**ISBN:**1522500308**Category:**Design**Page:**924**View:**1008

Visual computing and descriptive geometry are multidisciplinary fields addressing the handling of images, 3D models, and other computer graphics. These ideas are experiencing a revival due to emergent technologies and applications available to developers. Based in traditional forms of design and architecture, these fields are currently experiencing a bounty of new research based on old principles. The Handbook of Research on Visual Computing and Emerging Geometrical Design Tools seeks to add to this knowledge base by considering these technologies from a designer’s perspective rather than reiterating the principles of computer science. It combines aspects of geometry and representation with emerging tools for CAD, generation, and visualization while addressing the digital heritage of such fields. This book is an invaluable resource for developers, students of both graphic and computer-generated design, researchers, and designers.