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
7 - Self-Similar Sets
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
Self-similar sets are a special case of IFS attractors and have been studied extensively in the literature. In this chapter we consider self-similar sets and measures in detail. We will see that the Assouad dimension may be strictly larger than the Hausdorff dimension.
- Type
- Chapter
- Information
- Assouad Dimension and Fractal Geometry , pp. 93 - 109Publisher: Cambridge University PressPrint publication year: 2020