Let Formula: see text be a real number, we consider a class Formula: see text of two-dimensional homogeneous self-similar sets Formula: see text such that a pair of copies overlap. Based on the configuration concept by 1, we prove that Formula: see text, where Formula: see text is the largest positive root of the equation Formula: see text for some positive integers Formula: see text with Formula: see text.
Shaza Nammoura (Fri,) studied this question.