A random dot stereogram is a picture that looks like snow on a TV. By training your eye muscles to behave in a certain way, a 3-D image will magically appear. I do not know the specific optical properties that cause this to work. All I know is that it does. First, a little background on how our eyes work. Our eyes are focusing instruments, just like a camera lens, or the Hubble Telescope (except the Hubble can't see as far). If you stand on the sidewalk and look at your house, and then hold your finger at eye level with your arm fully extended. Now, close one eye. You can now focus your open eye so that your finger will be clear, but your house will be blurry. You can then make the house clear, and your finger will become blurry. This is called focus. The way we perceive depth is by the angle between our eyes. In other words, the further an object is from you the closer the line of site of your eyes is to being parallel. To see the stereogram, you need to angle your eyes as though you are looking at something twice as far away as the paper (or monitor). BUT, your eyes need to be focused at the surface of the paper, beacuase when it comes right down to it, that is where the image actually is, on the paper. It will take some practice. Your eye muscles aren't doing anything they haven't before, you just need to train them. Some of you may have seen these in magazines, or malls, where there were two dots above the image. These can be a big help. Hold your finger behind the paper just above the dots. Slowly pull your finger away, keeping your eyes focused on your finger, until the two dots turn into four dots and then the two middle dots merge into one, so you see three dots. Keep in mind that you must keep your eyes focused on your finger. You will see the two, or three or four, dots in your peripheral vision. When you have the three dots, you should see the image from your peripheral vision. Then you can slowly move your eyes down the page to see the rest of the image. A note about the dots: If you look at the image, you will see a pattern repeating itself several times across the page. The space between the two dots corresponds to the width of the repeating pattern. In the pictures generated by RDS, this distance is always one eigth of the width of the picture.
This is an RDS of the Mandelbrot set.