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