Let the two pictures become one... then you have 3D stereo vision!
How to see this annoying stuff:
Try this:
Let your eyes focus beyond the surface you're looking at. Where the pattern is similar you let them reconverge. No sudden eye movements.
Or this:
To get your eyes in unfocused mode, close them and look forward facing the screen. When you reopen them they won't be locked together on a specific point; they will both be looking straight forward. Don't let them converge quite so quickly. Again, look for that similar pattern (there's always one) and let them become one, then, without any sudden movements, look around.
You'll see dimensions, it's uncanny. It's like cardboard cutouts, but the background has dimension!!! If you go back to Jack Web the words below the eyes takes you to a site with other stereograms. Check it out.