Obligatory reference to Gödel, Escher and Bach.<p>(For the record, I do understand this article explores a different mathematical aspect of Escher than Hofstadter)
I've seen Lenstra's talk about Escher's print gallery some years ago in Rome and then again after a few months in Pisa.<p>One of the most captivating talks I've ever seen. He's a great speaker. I wish I had him as a professor.<p>EDIT: forgot to add, in the Mathematica blog there is another explanation of the mathematics between the "Droste effect" and the code to obtain it: <a href="http://blog.wolfram.com/2009/04/24/droste-effect-with-mathematica/" rel="nofollow">http://blog.wolfram.com/2009/04/24/droste-effect-with-mathem...</a>
I'm just speechless about that computed re-creation assembling the four frames. Brilliant.<p>The interpretation of the blank spot is also quite nice and very Escher-esque, with the content literally jumping out of the frame. Probably Escher left the center patch blank because his construction method would have him exceed some technical/physical limitation, so instead of drawing an approximation he preferred a void.
There's an OS X screensaver based on this work which animates the effect, in a similar way to "dive" animations into fractal images. Fascinating but also nauseating after a while.<p><a href="http://wakaba.c3.cx/s/lotsablankers/lotsaescher" rel="nofollow">http://wakaba.c3.cx/s/lotsablankers/lotsaescher</a>