Fractal geometry of Bedford-McMullen carpets
Jonathan M. Fraser
TL;DR
This paper surveys the fractal geometry of Bedford-McMullen carpets, focusing on their dimension theory and their significance in non-conformal dynamics and fractal geometry research.
Contribution
It provides a comprehensive overview of the dimension theory related to Bedford-McMullen carpets, highlighting their mathematical properties and research developments.
Findings
Detailed analysis of Hausdorff and box dimensions of carpets
Connections between carpets and non-conformal dynamical systems
Summary of recent advances in fractal geometry of these sets
Abstract
In 1984 Bedford and McMullen independently introduced a family of self-affine sets now known as \emph{Bedford-McMullen carpets}. Their work stimulated a lot of research in the areas of fractal geometry and non-conformal dynamics. In this survey article we discuss some aspects of Bedford-McMullen carpets, focusing mostly on dimension theory.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsMathematical Dynamics and Fractals · Topological and Geometric Data Analysis · Morphological variations and asymmetry