Escher “Print gallery” metapixel
This one uses a conformal transformation like Escher did in his “Print Gallery“:
A picture that contains a scaled-down copy of itself is periodic both in theta and in log (r). Taking the complex log of such an image gives a rectangular tiling of the plane; by scaling and rotating, I got a new tiling, then exponentiated it. Now going around 2 pi radians takes you diagonally across the original rectangle, so you end up one level away from where you started.
[Edit] See also these better versions.