The animated GIF files below were created with Mathematica, then tweaked with Microsoft GIF Animator. The Mathematica code used to generate these pictures is in the [NB] BeetleTracks.nb notebook.

These images show the changing paths of the beetles as they spiral in to the "counter-clockwise beetle center" of the triangle, as the shape of the triangle changes. (That is, the beetles are chasing one another counter-clockwise around the triangle.)

varying height varying location of peak varying side length varying angle