  We study the motion of $N$ particles moving on a two-dimensional triangular
lattice, whose sites are occupied by either left or right rotators. These
rotators deterministically scatter the particles to the left (right), changing
orientation from left to right (right to left) after scattering a particle.
This interplay between the scatterers and the particle's motion causes a single
particle to propagate in one direction away from its initial position. For
multiple particles we show that the particles' dynamics can be vastly
different. Specifically, we show that a particle can become entangled with
another particle potentially causing the particle's trajectory to become
periodic and that this can happen when the particles have the same or differing
speeds. We describe two classes of periodic orbits based on the particles'
initial velocities. We also describe how a particle with an unbounded past
trajectory implies that some, possibly other, particle(s) has an unbounded
future trajectory in this and other related multiparticle models.
