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
8 - Self-Affine 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-affine sets are another special case of IFS attractors. Since the defining maps may contract distance by different amounts in different directions, the dimension theory of self-affine sets and measures is more complicated, and much richer, than that of self-similar sets. In this chapter we study self-affine sets in detail, paying particular attention to Bedford–McMullen carpets where our theory can be developed explicitly.
Keywords
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- Information
- Assouad Dimension and Fractal Geometry , pp. 110 - 136Publisher: Cambridge University PressPrint publication year: 2020