Dimensions of the Boundaries of Self-Similar Sets
We introduce a finite boundary type condition on iterated function systems of contractive similitudes on Rd. 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.
Lau, Ka-Sing, Sze-Man Ngai.
"Dimensions of the Boundaries of Self-Similar Sets."
Experimental Mathematics, 12 (1): 13-26.