Hausdorff Dimension of Self-Similar Sets with Overlaps
Journal of London Mathematical Society
The notion of ‘finite type’ iterated function systems of contractive similitudes is introduced, and a scheme for computing the exact Hausdorff dimension of their attractors in the absence of the open set condition is described. This method extends a previous one by Lalley, and applies not only to the classes of self-similar sets studied by Edgar, Lalley, Rao and Wen, and others, but also to some new classes that are not covered by the previous ones.
Ngai, Sze-Man, Yang Wang.
"Hausdorff Dimension of Self-Similar Sets with Overlaps."
Journal of London Mathematical Society, 63 (3): 655-672.