THE FIRST RANDOM dot stereogram was invented by Dr. Bela Julesz in 1959 as an experiment to test stereopsis, the ability to see in 3D. By using a random dot pattern, Julesz eliminated the depth cues that are inherent in recognizable images.
Consider this example. First create a rectangle of randomly arranged dots. (fig 1). Within that rectangle select a group of dots that make up a small shape. In this example the small shape is a circle and the selected dots are the dots that fall within the blue circle. (fig. 2).
Next, create a new rectangle identical to the original rectangle, except that the dots within the small shape have been shifted to the left. (fig. 3). When the two rectangles are viewed together as a stereo pair, the image of the circle appears to float above the background. (fig. 4).
In 1979 Christopher Tyler discovered that the offset scheme could be applied to a single image. This was the birth of the single image random dot stereogram (fig. 5).
DEPTH PERCEPTION depends on having two eyes. Most people who have depth perception can see a Magic Eye image. People with impaired depth perception or people who have one eye which is extremely dominant (as in amblyopia) will have more difficulty seeing the image. If you are having trouble, feel free to e-mail us. We can suggest several different methods to give you the best chance to see 3D.
SEEING IN 3D is an effort in relaxation and defocusing. The example below is very easy to see. First, gaze at the two circles that are positioned above the Magic Image. Let your eyes defocus (see double) until you see four dots. Next, make the two middle dots overlap so that you seem to see only three dots. Concentrate on the middle dot. When the middle dot seems clear, you will be perfectly diverged to view a Magic Eye image. Allow your eyes to drift down to the image and you will see the hidden image inside the pattern. In this case the image is a flattened sphere.
A MAGIC EYE IMAGE is seen by allowing the eyes to diverge, as if you're focused on an object more distant than the printed page. If you cross your eyes you will also see 3D, but you will invert the image (see the image inside out). Crossing may also strain the eyes. The normal diverging technique can actually help you learn to relax your eyes
A MAGIC EYE IMAGE is normally viewed at a divergence distance equal to the width of one repeat of the 2D "starter" pattern. If you're good at diverging, you can diverge your eyes twice that distance. This will cause you to see multiple, distorted hidden objects in 3D.
HERE ARE SOME MORE EXAMPLES:
Exerts Taken From www.magiceye.com.