Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgements
- Part One Theory
- Part Two Examples
- 6 Iterated Function Systems
- 7 Self-Similar Sets
- 8 Self-Affine Sets
- 9 Further Examples: Attractors and Limit Sets
- 10 Geometric Constructions
- 11 Two Famous Problems in Geometric Measure Theory
- 12 Conformal Dimension
- Part Three Applications
- References
- List of Notation
- Index
6 - Iterated Function Systems
from Part Two - Examples
Published online by Cambridge University Press: 13 October 2020
Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgements
- Part One Theory
- Part Two Examples
- 6 Iterated Function Systems
- 7 Self-Similar Sets
- 8 Self-Affine Sets
- 9 Further Examples: Attractors and Limit Sets
- 10 Geometric Constructions
- 11 Two Famous Problems in Geometric Measure Theory
- 12 Conformal Dimension
- Part Three Applications
- References
- List of Notation
- Index
Summary
One of the most important and widely used methods for constructing fractal sets is via iterated function systems. These were introduced in a celebrated article of Hutchinson from 1980. We consider the special case of self-similar sets in Chapter 7, self-affine sets in Chapter 8, and self-conformal sets in Section 9.1, but in this chapter we introduce the theory of iterated function systems and their attractors in full generality.
Keywords
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- Information
- Assouad Dimension and Fractal Geometry , pp. 81 - 92Publisher: Cambridge University PressPrint publication year: 2020