Mr. Fujiki has written a 3D display / collision engine that simulates the impossible spatial logic from the work of M.C. Escher. The reality of the autonomous character is affected by how his reality looks to you, the observer. If you don't see a gap, the character doesn't experience one. If you see two platforms touching, the character can cross.
I did not fully grasp it until I saw the video, which I highly recommend. Not only does it show very clearly what is going on, it also is a very nicely made video in itself.
It should be possible to make a puzzle game based on this technology. A constrained set of possibilities to place objects in 3D, combined with choosing the right angle to enable a connection from A to B.
You can even download the software if you have a PC with DirectX 9 installed. There's also a Java applet, but it ran too slow for me. Pity.
(Via Andrew Armstrong.)
Update: As was pointed out in the comments, this technology has been turned into a downloadable PS3 game called Echochrome. You can read a preview from the 2007 Tokyo Game Show here. Thanks Andreas and Nur-ab-sal!