Escher and the Droste effect



The pictures below show for a grid how the Droste picture (bottom left) is transformed to a picture like Escher's Print Gallery. The top two pictures have a tiling symmetry, and they allow the same vertical shift. The map between them is a rotation by about 41 degrees counter clockwise and scaling by about 75%. The vertical transformations are the exponential map [] on the plane of complex numbers [].

Different choices of the horizontal map which rotates and scales lead to many different images.

See our article [PDF] in the Notices of the AMS for the full mathematical story.