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