We start a photon in the equatorial plane, = , and with direction radially inwards, = (-0.5,0,0). Therefore, it will stay in the equaorial plane.
We integrate the geodesic equation in 300 steps, using a step size = 0.20
In this movie, we vary the rotation parameter a/M from 0.00 (no rotation) to 1.00 (the most extreme rotation possible). In every frame of the movie, we show a null godesic, that is, the trajectory of a photon, so it's proper time axis is along the geodesic, so to speak, and has nothing to do with the time axis of the movie, which shows a change in a/M.
The IDL script is mf_01.
Note: this movie has a minor problem: frame 000 and 001 are identical, except for the annotation text. This is because something went wrong when running Explorer. The Inventor (and VRML) files are different.