Fractals Everywhere

ISBN-10: 0486488705

ISBN-13: 9780486488707

Edition: 3rd 2012 (Revised)

List price: $54.00 Buy it from $19.62
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Focusing on how fractal geometry can be used to model real objects in the physical world, this up-to-date edition contains a new chapter on recurrent iterated function systems, problems and tools emphasizing fractal applications, and an answer key. A bonus CD featuring Barnsley's Desktop Fractal Design Systemserves as an excellent supplement. "Technically excellent, informative, and entertaining." — Robert McCarty. 32-page full-color insert.
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Book details

List price: $54.00
Edition: 3rd
Copyright year: 2012
Publisher: Dover Publications, Incorporated
Publication date: 7/17/2012
Binding: Mixed Media
Pages: 560
Size: 7.00" wide x 8.50" long x 1.25" tall
Weight: 2.046
Language: English

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