Here's a link to explain it further http://ofb.net/~whuang/imgs/spin/

(This may also explain why it is so hard to make it switch direction on will without covering parts of the image, since your brain picks up on these tiny details and uses them to process the image.)

It's another version of this using a cat, and it's a bit easier to manage…

Simply focus on the cats front (or top) legs, then at the moment they overlap into the cats body trick your mind to switch the direction……picturing the legs as moving front to back instead of side to side helps me.

I have even been able to make the cat dance from side to side without ever turning all the way around.

It’s just a shadow. You can’t really tell if the image is facing forward or backward, but since we are used to people looking at us, our first impression is that the dancer is looking at us. The dancer’s leg is moving left, stops, right, stops etc. If on the split-second your eyes saw the image, the dancer’s leg was moving left – you would think that she was spinning clockwise. If it was moving right – you would think that she was spinning counter-clockwise. From that point, your brain had already decided which direction the dancer was spinning and it would be very difficult to change your mind without looking away. It is about the exact split-second your eyes first saw the image.

How’s my theory?