## Tsukuba Journal of Mathematics

### Pisot substitutions and the Hausdorff dimension of boundaries of atomic surfaces

#### Abstract

The atomic surface $X_q$ from an unimodular Pisot substitution $\sigma$ usually has the fractal boundary and it generates a selfaffine tiling. In this paper, we study the boundary $\partial X_{q}$ as the graph directed self-affine fractal and estimate the Hausdorff dimension of the boundary.

#### Article information

Source
Tsukuba J. Math., Volume 30, Number 1 (2006), 195-223.

Dates
First available in Project Euclid: 30 May 2017

Permanent link to this document
https://projecteuclid.org/euclid.tkbjm/1496165037

Digital Object Identifier
doi:10.21099/tkbjm/1496165037

Mathematical Reviews number (MathSciNet)
MR2248292

Zentralblatt MATH identifier
1130.37318

#### Citation

Feng, De-Jun; Furukado, Maki; Ito, Shunji. Pisot substitutions and the Hausdorff dimension of boundaries of atomic surfaces. Tsukuba J. Math. 30 (2006), no. 1, 195--223. doi:10.21099/tkbjm/1496165037. https://projecteuclid.org/euclid.tkbjm/1496165037