No flies on Rama: The flying bugs illusion
These two bugs fly clockwise along circular orbits of the same size, in all 3 movies. They are in counter phase; one is at 6 o’clock when the other is at 12 o’clock.

The orbits look elliptical, wide on the left and tall on the right.  The background moves CCW and is in counter-phase with the horizontal components of the left fly but the vertical components of the right fly.