AbstractThe motion of an arbitrary set of points in a plane chasing one another in cyclic pursuit is studied. Given a set of labeled points 1, 2, 3,…,n, with coordinates (x1, y1), (x2, y2,),…, (xn, yn), it is arranged for point (xi, yi) to chase point (xi+1, yi+1) along the instantaneous line joining them. To close the cycle, point (xn, yn) chases point (x1, y1). All points move with the same speed. The motion just described is called motion in“forward time.”If the sign of the time derivative operator is changed, with the result that point (xi, yi,) runs away from point (xi+1, yi+1), the motion is called motion in“reverse time.”Motion in both forward and reverse time is studied with the aid of a computer program. In forward time, it is observed that ultimately, in almost all cases tried, the points become collinear, with large maximum-to-minimum distance ratio, regardless of the shape of the initial configuration. In reverse time, it is observed that the points ultimately arrange themselves in a star pattern, with the star vertex angle less than some number in the vicinity of ninety degrees. By an analysis based on the stability of the equations of motion, the exact value of the maximum star angle is computed, as a function of the number of points.