In this paper, we investigate the scatter problem, which is defined as follows: Given a set of n robots, regardless of the initial position of the robots on the plane, eventually, no two robots are located at the same position forever. We show that this problem cannot be deterministically solved. Next, we propose a randomized algorithm. The proposed solution is trivially self-stabilizing. We then show how to design a self-stabilizing version of any deterministic solution for the Pattern Formation and the Gathering problems for any number n ≥ 2 of robots.