  We consider the dynamics of light rays in triangle tilings where triangles
are transparent and adjacent triangles have equal but opposite indices of
refraction. We find that the behavior of a trajectory on a triangle tiling is
described by an orientation-reversing three-interval exchange transformation on
the circle, and that the behavior of all the trajectories on a given triangle
tiling is described by a polygon exchange transformation. We show that, for a
particular choice of triangle tiling, certain trajectories approach the Rauzy
fractal, under rescaling.
