  Numerical computations suggest that each point on a certain optimized shape
called the ideal trefoil is in contact with two other points. We consider
sequences of such contact points, such that each point is in contact with its
predecessor and call it a billiard. Our numerics suggest that a particular
billiard on the ideal trefoil closes to a periodic cycle after nine steps. This
cycle also seems to be an attractor: all billiards converge to it.
