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Introduction to the Dover Edition | |
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Foreword to the Second Edition | |
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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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M�bius 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 | |