This animation set is based on the original work by ???*. The original image of a dancer in a perpetual spin can be interpreted two different ways - she can either be spinning in a clockwise direction, or in a counter-clockwise direction (imagine her spinning on a clock face). Some people's perception may favor one direction over the other, and some people may see her change directions from time to time. The fact is that the image is a constant 34-frame loop representing 1 full revolution of the dancer, and no trickery is used to make her seem to be spinning one way or the other at any point in time. The effect is entirely caused by the perception of the viewer as he or she interprets the ambiguous frames where the spinning dancer's body appendages (legs and arms) cross over each other.
To prove this, shown above are two copies of the original .gif animation, each having the same 34 frames representing 1 full revolution of the spinning dancer. The only difference between the left and right image is that on the left, I have added gray lines in the leg area to imply that the dancer is standing on her left leg and spinning in a clockwise direction. On the right, gray lines have been added in the leg area to imply that the dancer is standing on her right leg and spinning in a counter-clockwise direction. By adding this information to the animation, the variable of viewer perception is removed from the process, and when looking at only one image at a time (cover the other with your hand), it is believable that the dancer is only spinning in a single direction. Viewing both images together, side by side, will prove to you that it is the identical (original) animation.
*This original story, to the best of my knowledge, can be found at news.com.au, and courtesy of "AAP". I would very happily credit the individual(s) who constructed this animation, but i can find no such reference or record.
Editing of the original by Matthew Lewis for the benefit of a few friends who were loosing their minds.