Today I came across this rather neat right brain versus left brain test via John Gruber. So I look at it and see the dancer turning anti-clockwise, and then head over to the text of the article to find out what it means. However, for no good reason, my eye flicks back to the dancer again and she's changed direction! (now going clockwise). Hmm…
Apparently, the direction you perceive corresponds to which side of your brain is more heavily used. Anti-clockwise corresponds to the left side (the more common according to the article), and clockwise for the right side. The general gist seems to be that those who use the right side of the brain are of the "arty" variety.
The article continues on to say that you can try to focus and change the direction of the animation. Well I tried this, but to no avail. However, I keep switching away from the image and then coming back; often it's changed direction with no effort on my part. I guess this explains why I'm such an indecisive person!