Assouad and lower dimensions of graph-directed Bedford–McMullen carpets
Abstract
We calculate the Assouad and the lower dimensions of graph-directed Bedford–McMullen carpets, which reflect the extreme local scaling laws of the sets, in contrast to known results on Hausdorff and box dimensions. We also investigate the relationship between distinct dimensions. In particular, we identify an equivalent condition when the box and the Assouad dimensions coincide, and show that under this condition, the Hausdorff dimension attains the same value.
Fields of Study & Subjects
Computational Geometry and Mesh Generation
Publication details
- Journal / source
- Journal of Fractal Geometry Mathematics of Fractals and Related Topics
- Volume
- 13
- Issue
- 3
- Pages
- 321–352
- Publication date
- 2 June 2026
- Language
- EN