I got this information from the Uni' of NSW when I passed this link around last week -
Initial direction is a function of where you look in the figure plus some random variables (which probably do NOT include brain dominance since the L side of fixation goes to the right brain and the R of fixation goes to the Left brain. If you stare at the center of the figure it goes 50/50. Fix at either side and you can bias it but it doesn't affect the frequency of the two directions).
If the movement was continuous it would reverse regularly. This usually occurs at pauses and changes in fixation. This figure pauses regularly and this can trigger reversal. With very steady fixation, another phenomenon occurs - you can actually see other patterns of movement such as expansion contraction without depth and even multiple figures with delay lags.
I have a paper on it (one of my first:- Vaegan. Two parameters measure perceptual transformations during monotonous stimulation. Quart. J. Exptl. Psychol., 1976;28:583-589).
Both effects are caused by adaptation/inhibition. Reversals / changes of state are caused when movement of fixation releases inhibition and evokes the opposite. Multiple state are caused by increasing inhibition / adaptation of all previous states. The two parameters are independent and a function of the individual.