The Spinning Dancer, also known as the silhouette illusion, is a kinetic, bistable optical illusion resembling a pirouetting female dancer. The illusion, created in 2003 by web designer Nobuyuki Kayahara, involves the apparent direction of motion of the figure. Some observers initially see the figure as spinning clockwise (viewed from above) and some counterclockwise.
The illusion derives from the lack of visual cues for depth. For instance, as the dancer’s arms move from viewer’s left to right, it is possible to view her arms passing between her body and the viewer (that is, in the foreground of the picture, in which case she would be circling counter-clockwise on her right foot) and it is also possible to view her arms as passing behind the dancer’s body (that is, in the background of the picture, in which case she is seen circling clockwise on her left foot).
When she is facing to the left or to the right, her breasts and ponytail clearly define the direction she is facing, although there is ambiguity in which leg is which. However, as she moves away from facing to the left (or from facing to the right), the dancer can be seen (by different viewers, not by a single individual) facing in either of two directions. At first, these two directions are fairly close to each other (both left, say, but one facing slightly forward, the other facing slightly backward) but they become further and further away from each other until we reach a position where her ponytail and breasts are in line with the viewer (so that neither her breasts nor her ponytail are seen so readily). In this position, she could be facing either away from the viewer or towards the viewer, so that the two positions two different viewers could see are 180 degrees apart.
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Update (2/3/13): The Spinning Dancer Illusion Explained