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| FRACTALS EVERYWHERE
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 To order this title, and for more information, click here
By
Michael Barnsley
Description
This volume is the second edition of the highly successful Fractals Everywhere. The Focus of this text is how fractal geometry can
be used to model real objects in the physical world.
This edition of Fractals Everywhere is the most up-to-date fractal textbook
available today.
Fractals Everywhere may be supplemented by Michael F. Barnsley's Desktop Fractal Design System (version 2.0) with
IBM for Macintosh software. The Desktop Fractal Design System 2.0 is a tool for designing Iterated Function Systems codes and fractal
images, and makes an excellent supplement to a course on fractal geometry
Contents
Foreword
Acknowlegments
Chapter I - Introduction
Chapter II - Metric Spces; 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: The Place where Fractals Live
7. The Completeness of the Space of Fractals
8. 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. Mobius 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
Theorem
11. Blowing in the Wind: The Continuous Dependence of Fractals on Parameters
Chapter IV - Chaotic Dynamics on Fractals
1. The Address 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 Fractals
Chapter 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 Set
2. 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
1. Introduction to Invariant Measures on Fractals
2. Fields and Sigma-Fields
3. Measures
4. Integration
5. The Compact Metric
Space (P(X),d)
6. A contraction Mapping on (P(X))
7. Elton's Theorem 364
8. Application to Computer Graphics
Chapter X - Recurrent
Iterated Function Systems
1. Fractal Systems
2. Recurrent Iterated Function Systems
3. Collage Theorem for Recurrent Iterated
Function Systems
4. Fractal Systems with Vectors of Measures as Their Attractors
5. References
References
Selected Answers
Index
Credits for Figures and Color Plates
| Bibliographic details |
Paperback, 534 pages, publication date: APR-2000
ISBN-13: 978-0-12-079069-2
ISBN-10: 0-12-079069-6
Imprint: MORGAN KAUFFMAN
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| Price and Ordering |
Price:
EUR 71.95
USD 82.95
GBP 47.99
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Last update: 27 Sep 2008
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