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Introduction to the Dover Edition | p. xi |
Foreword to the Second Edition | p. xv |
Acknowledgments | p. xvii |
Introduction | p. 1 |
Metric Spaces; Equivalent Spaces; Classification of Subsets; and the Space of Fractals | p. 5 |
Spaces | p. 5 |
Metric Spaces | p. 10 |
Cauchy Sequences, Limit Points, Closed Sets, Perfect Sets, and Complete Metric Spaces | p. 15 |
Compact Sets, Bounded Sets, Open Sets, Interiors, and Boundaries | p. 19 |
Connected Sets, Disconnected Sets, and Pathwise-Connected Sets | p. 24 |
The Metric Space (H(X), h):The Place Where Fractals Live | p. 27 |
The Completeness of the Space of Fractals | p. 33 |
Additional Theorems about Metric Spaces | p. 40 |
Transformations on Metric Spaces; Contraction Mappings; and the Construction of Fractals | p. 42 |
Transformations on the Real Line | p. 42 |
Affine Transformations in the Euclidean Plane | p. 49 |
Möbius Transformations on the Riemann Sphere | p. 58 |
Analytic Transformations | p. 61 |
How to Change Coordinates | p. 68 |
The Contraction Mapping Theorem | p. 74 |
Contraction Mappings on the Space of Fractals | p. 79 |
Two Algorithms for Computing Fractals from Iterated Function Systems | p. 84 |
Condensation Sets | p. 91 |
How to Make Fractal Models with the Help of the Collage Theorem | p. 94 |
Blowing in the Wind: The Continous Dependence of Fractals on Parameters | p. 101 |
Chaotic Dynamics on Fractals | p. 115 |
The Addresses of Points on Fractals | p. 115 |
Continuous Transformations from Code Space to Fractals | p. 122 |
Introduction to Dynamical Systems | p. 130 |
Dynamics on Fractals: Or How to Compute Orbits by Looking at Pictures | p. 140 |
Equivalent Dynamical Systems | p. 145 |
The Shadow of Deterministic Dynamics | p. 149 |
The Meaningfulness of Inaccurately Computed Orbits is Established by Means of a Shadowing Theorem | p. 158 |
Chaotic Dynamics on Fractals | p. 164 |
Fractal Dimension | p. 171 |
Fractal Dimension | p. 171 |
The Theoretical Determination of the Fractal Dimension | p. 180 |
The Experimental Determination of the Fractal Dimension | p. 188 |
The Hausdorff-Besicovitch Dimension | p. 195 |
Fractal Interpolation | p. 205 |
Introduction: Applications for Fractal Functions | p. 205 |
Fractal Interpolation Functions | p. 208 |
The Fractal Dimension of Fractal Interpolation Functions | p. 223 |
Hidden Variable Fractal Interpolation | p. 229 |
Space-Filling Curves | p. 238 |
Julia Sets | p. 246 |
The Escape Time Algorithm for Computing Pictures of IFS Attractors and Julia Sets | p. 246 |
Iterated Function Systems Whose Attractors Are Julia Sets | p. 266 |
The Application of Julia Set Theory to Newton's Method | p. 276 |
A Rich Source for Fractals: Invariant Sets of Continuous Open Mappings | p. 287 |
Parameter Spaces and Mandelbrot Sets | p. 294 |
The Idea of a Parameter Space: A Map of Fractals | p. 294 |
Mandelbrot Sets for Pairs of Transformations | p. 299 |
The Mandelbrot Set for Julia Sets | p. 309 |
How to Make Maps of Families of Fractals Using Escape Times | p. 317 |
Measures on Fractals | p. 330 |
Introduction to Invariant Measures on Fractals | p. 330 |
Fields and Sigma-Fields | p. 337 |
Measures | p. 341 |
Integration | p. 344 |
The Compact Metric Space (P(X), d) | p. 349 |
A Contraction Mapping on (P(X)) | p. 350 |
Elton's Theorem | p. 364 |
Application to Computer Graphics | p. 370 |
Recurrent Iterated Function Systems | p. 379 |
Fractal Systems | p. 379 |
Recurrent Iterated Function Systems | p. 383 |
Collage Theorem for Recurrent Iterated Function Systems | p. 392 |
Fractal Systems with Vectors of Measures as Their Attractors | p. 403 |
References | p. 409 |
References | p. 412 |
Selected Answers | p. 416 |
Index | p. 523 |
Credits for Figures and Color Plates | p. 533 |
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