Stuttering Cantor-like random sets

In each step of the construction of the Cantor set we consider two complementary operations: in the first stage (damage) the middle step of each remaining segment is deleted; in the second stage (random repair) an uniform random segment is united to what remains after deletion. We compute the Hausdorff dimension of the limiting fractal obtained as the intersection of the sets obtained in the ad infinitum repetition of this stammering iterative procedure, which as expected is bigger than the Hausdorff dimension of the classical middle Cantor set with no repair. Stuttering random Cantor sets are obtained using deletion of uniform random segments both in the damage and in the repair stages in each step of the iterative procedure. The use of general beta random segments in the stuttering construction of Cantor-like random sets is also discussed.