Geodesic
Lacunary self-similar fractal sets and intersection of cantor sets
Lobachevskii journal of mathematics, Tome 12 (2003), pp. 41-50.

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The problem on intersection of Cantor sets was examined in many papers. To solve this problem, we introduce the notion of lacunary self-similar set. The main difference to the standard (Hutchinson) notion of self-similarity is that the set of similarities used in the construction may vary from step to step in a certain way. Using a modification of method described in [3], [4], we find the Hausdorff dimension of a lacunary self-similar set. 
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K. B. Igudesman. Lacunary self-similar fractal sets and intersection of cantor sets. Lobachevskii journal of mathematics, Tome 12 (2003), pp. 41-50. http://geodesic.mathdoc.fr/item/LJM_2003_12_a2/

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