无处不在的分形（第2版）

　　I acknowledge and thank many people for their help with this book. In particular I thank Alan Sloan， who has unceasingly encouraged me， who wrote the first Collage software， and who so clearly envisioned the application of iterated function systems to image compression and communications that he founded a company named Iterated Systems Incorporated. Edward Vrscay， who taught the first course in deterministic fractal geometry at Georgia Tech， shared his ideas about how the course could be taught， and suggested some subjects for inclusion in this text. Steven Demko， who collaborated with me on the discovery of iterated function systems， made early detailed proposals on how the subject could be presented to students and scientists， and provided comments on several chapters. Andrew Harrington and Jeffrey Geronimo， who discovered with me orthogonal polynomials on Julia sets. My collaborations with them over five years formed for me the foundation on which iterated function systems are built. Watch for more papers from us！Les Karlovitz， who encouraged and supported my research over the last nine years， obtained the time for me to write this book and provided specific help， advice， and direction. His words can be found in some of the sentences in the text. Gunter Meyer， who has encouraged and supported my research over the last nine years. He has often given me good advice. Robert Kasriel， who taught me some topology over the last two years， corrected and rewrote my proof of Theorem 7.1 in Chapter II and contributed other help and warm encouragement. Nathanial Chafee， who read and corrected Chapter II and early drafts of Chapters III and IV. His apt constructive comments have increased substantially the precision of the writing. John Elton， who taught me some ergodic theory， continues to collaborate on exciting research into iterated function systems， and helped me with many parts of the book. Daniel Bessis and Pierre Moussa， who are filled with the wonder and mystery of science， and taught me to look for mathematical events that are so astonishing that they may be called miracles. Research work with Bessis and Moussa at Saclay during 1978， on the Diophantine Moment Problem and Ising Models， was the seed that grew into this book. Warren Stahle， who provided some of his experimental research results.

暂缺《无处不在的分形（第2版）》作者简介

Foreword.
Acknowledgments
Chapter Ⅰ Introduction
Chapter Ⅱ Metrlc Spaces; Equlvolent Spaces; Clossificatlon of Subsets; and the Space of Froctols
1.Spaces
2.Metric Spaces
3.Cauchy Sequences, Limit Points, Closed Sets, Perfect Sets, and Complete Metric Spaces
4.Compact Sets, Bounded Sets, Open Sets, Interiors, and Boundaries
5.Connected Sets, Disconnected Sets, and Pathwise- Connected Sets
6.The Metric Space (74(X), h): The Place Where Fractals Live
7.The Completeness of the Space of Fractals
8.Additional Theorems about Metric Spaces
Chapter Ⅲ Transformations on Metric Spaces; Contraction Mappings; and the Construction of Fractals
1.Transformations on the Real Line
2.Affine Transformations in the Euclidean Plane
3.MObius Transformations on the Riemann Sphere
4.Analytic Transformations
5.How to Change Coordinates
6.The Contraction Mapping Theorem
7.Contraction Mappings on the Space of Fractals
8.Two Algorithms for Computing Fractals from Iterated Function Systems
9.Condensation Sets
10.How to Make Fractal Models with the Help of the Collage Theorem
11.Blowing in the Wind: The Continous Dependence of Fractals on Parameters
Chapter Ⅳ Chaotic Dynamics on Fractals
1.The Addresses of Points on Fractals
2.Continuous Transformations from Code Space to Fractals
3.Introduction to Dynamical Systems
4.Dynamics on Fractals: Or How to Compute Orbits by Looking at Pictures
5.Equivalent Dynamical Systems
6.The Shadow of Deterministic Dynamics
7.The Meaningfulness of Inaccurately Computed Orbits is Established by Means of a Shadowing Theorem
8.Chaotic Dynamics on Fractals
Chapter Ⅴ Fractal Dimension
1.Fractal Dimension
2.The Theoretical Determination of the Fractal Dimension
3.The Experimental Determination of the Fractal Dimension
4.The Hausdorff-Besicovitch Dimension
Chapter Ⅵ FrocIoI Interpolation
1.Introduction: Applications for Fractal Functions
2.Fractal Interpolation Functions
3.The Fractal Dimension of Fractal Interpolation Functions
4.Hidden Variable Fractal Interpolation
5.Space-Filling Curves
Chapter Ⅶ Julia Sets
1.The Escape Time Algorithm for Computing Pictures of IFS Attractors and Julia Sets
2.Iterated Function Systems Whose Attractors Are Julia Sets
3.The Application of Julia Set Theory to Newton's Method
4.A Rich Source for Fractals: Invariant Sets of Continuous Open Mappings
Chapter Ⅷ Parameter Spaces and Mandelbrot Sets
1.The Idea of a Parameter Space: A Map of Fractals
2.Mandelbrot Sets for Pairs of Transformations
3.The Mandelbrot Set for Julia Sets
4.How to Make Maps of Families of Fractals Using Escape Times
Chapter Ⅸ Measures on Fractals
1.Introduction to Invariant Measures on Fractals
2.Fields and Sigma-Fields
3.Measures
4.Integration
5.The Compact Metric Space (79(X), d)
6.A Contraction Mapping on (P(X))
7.Elton's Theorem
8.Application to Computer Graphics
Chapter Ⅹ Recurrent Iterated Function Systems
1.Fractal Systems
2.Recurrent Iterated Function Systems
3.Collage Theorem for Recurrent Iterated Function Systems
4.Fractal Systems with Vectors of Measures as Their Attractors
5.References
References
Selected Answers
Index