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## Details

Genre/Form: | Electronic books |
---|---|

Additional Physical Format: | Print version: Barnsley, Michael F. Fractals Everywhere : New Edition. Newburyport : Dover Publications, ©2013 |

Material Type: | Document, Internet resource |

Document Type: | Internet Resource, Computer File |

All Authors / Contributors: |
Michael F Barnsley |

ISBN: | 9780486320342 0486320340 |

OCLC Number: | 1041818845 |

Notes: | 1. Introduction to Invariant Measures on Fractals. |

Description: | 1 online resource (1174 pages). |

Contents: | Cover; Title Page; Copyright Page; Dedication; Contents; Introduction to the Dover Edition; Foreword to the Second Edition; Acknowledgments; Chapter I Introduction; Chapter II Metric Spaces; Equivalent Spaces; Classification of Subsets; and the Space of Fractals; 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 (H(X), h): The Place Where Fractals Live. 7. The Completeness of the Space of Fractals8. 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. Möbius 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 Theorem11. 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 FractalsChapter 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 Fractal 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 Sets2. 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. |

Series Title: | Dover books on mathematics. |

### Abstract:

"Difficult concepts are introduced in a clear fashion with excellent diagrams and graphs."--Alan E. Wessel, Santa Clara University"The style of writing is technically excellent, informative, and entertaining." - Robert McCartyThis new edition of a highly successful text constitutes one of the most influential books on fractal geometry. An exploration of the tools, methods, and theory of deterministic geometry, the treatment focuses on how fractal geometry can be used to model real objects in the physical world. Two sixteen-page full-color inserts contain fractal images, and a bonus CD of an IFS Generator provides an excellent software tool for designing iterated function systems codes and fractal images. Suitable for undergraduates and graduate students of many backgrounds, the treatment starts with an introduction to basic topological ideas. Subsequent chapters examine transformations on metric spaces, dynamics on fractals, fractal dimension and interpolation, Julia sets, and parameter spaces. A final chapter introduces measures on fractals and measures in general. Problems and tools emphasize fractal applications, and an answers section contains solutions and hints.

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