With no available lenses, I had to think out of the box. The use of lenses, reminded me of an old principle: that of a camera obscura. I have made one when I was young, and if anything, it taught me that at least for certain problems, a lens can be replaced by a small hole. That would work here too: get a piece of paper, make one-pixel-sized holes in it and hold it at a certain distance from the monitor. Through the one-pixel-sized holes, you could look at exactly one pixel, and because of the distance between the paper sheet and the monitor, the pixel you look at changes when you move your head around. That idea was adaptable to lenticular lenses too: make the holes into a narrow slit in e.g. a piece of paper and you should have the same effect. I later learned I wasn't the only one coming up with this: the paper-with-slits-in-it actually is called a parralax barrier.
Implementing the idea of the parralax barrier as paper-with-slits-in-it wasn't something I was planning on doing, though: cutting long slices out of a piece of paper with the precision of exactly one pixel on my LCD isn't my idea of a good pastime. So I thought it through a bit more and decided I needed the computer to do the job. Bring in a laserprinter and transparency sheets: if you generate an image that's all black except for small bars of white, you've got the same effect but pixel-precise and without too much work with a knife and magnifiers.
Long story short: I hacked together two scripts in PHP: one to generate the needed pattern to print on a transparency sheet, the other to combine a bunch of images so that the combined image would be viewable through the printed sheet. To make a long story (involving much hacking and messed-up transparency sheets) short: after shooting shooting pictures at multiple angles and combining these with the script, the result is someting like this:
The video itself, unfortunately, doesn't show the effect in all it's glory: first off all, the video is 2D while the image isn't, and secondly, the printed sheet interferes with the CCD of my camera creating ugly black interference-stripes. The important thing to notice is that the laptop displays 3 static images, which seem to change when I move the camera around. If you can create a better video of the effect, I'd gladly put that up.