Dimensions of the Boundaries of Self-Similar Sets

Authors

Ka-Sing Lau, The Chinese University of Hong KongFollow
Sze-Man Ngai, Georgia Southern UniversityFollow

Document Type

Article

Publication Date

2003

Publication Title

Experimental Mathematics

DOI

10.1080/10586458.2003.10504709

ISSN

1944-950X

Abstract

We introduce a finite boundary type condition on iterated function systems of contractive similitudes on R^d. Under this condition, we compute the Hausdorff dimension of the boundary of the attractor in terms of the spectral radius of some finite offspring matrix. We describe how to construct such a matrix. We also show that, in this case, the box dimension equals the Hausdorff dimension. In particular, this allows us to compute the Hausdorff dimension of the boundary of a class of self-similar sets defined by expansion matrices with noninteger entries.

Recommended Citation

Lau, Ka-Sing, Sze-Man Ngai. 2003. "Dimensions of the Boundaries of Self-Similar Sets." Experimental Mathematics, 12 (1): 13-26. doi: 10.1080/10586458.2003.10504709
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/605