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