The animated image is simply a white ball moving back and forth sinusoidally about 45 cycles per minute (four seconds for 3 cycles). On my monitor, the horizontal range of motion is about 2.6 inches (6.5 cm).
An ideal filter can be made from the two "lenses" of a pair of polaroid sunglasses. This is the best option because you can vary the darkness by rotating one of the "lenses" relative to the other. I broke apart a pair of clip-on polaroid sunglasses. If you have two pairs, you can use them together without having to break them.
Note submitted April 10, 2002 by Andi Karrer:
With an flat panel LCD or TFT display, this is even simpler. You need only one polaroid sunglass lens because the display is already polarized. Just hold one "lens" of a pair of polaroid sunglasses in front of one eye and rotate until the ball becomes appropriately dark.
The following (static) image illustrates a degree of darkening that works well for me:
The effect seems to increase as you view it longer. Moving back away from the screen may also be helpful.
For me, the ball appears to move in and out by a distance of about .75 inch (2 cm) from the screen.
With the filter over your left eye and the ball moving to the right, the two lines of sight converge at a point behind the screen. When the ball is moving to the left, the two lines of sight converge at a point in front of the screen.