| Description |
xii, 394 pages, 16 unnumbered pages of plates : illustrations (some color) ; 25 cm |
| Bibliography |
Includes bibliographical references (pages 381-384) and index. |
| Contents |
Metric Spaces; Equivalent Spaces; Classification of Subsets; and the Space of Fractals -- Spaces -- 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 -- Mobius 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. |
| Subject |
Fractals.
|
| Indexed Term |
Linear algebra |
| Other Form: |
Online version: Barnsley, M. F. (Michael Fielding), 1946- Fractals everywhere. Boston : Academic Press, c1988 (OCoLC)623917439 |
| ISBN |
0120790629 |
|
9780120790623 |
|
