Triangular patterns in groups of moving individuals

In this paper we discuss an exercise in systemic therapy. In a group of people, each person chooses two others to form an equilateral triangle with. Then, everyone starts moving to reach this goal. A stable state is defined as a state in which no persons are moving anymore. The research question is "Given initial conditions, does the system converge to a stable state?". We find that systems with a specific structure are stable and we find that out of sixty possible configurations with four people, fifty-five are stable.