Prentententoonstelling—or Print Gallery—is a recur­sive M. C. Escher draw­ing. For Math­e­mat­ics Aware­ness Month 2003, Escher and the Droste Effect delves into the math­e­mat­ics behind one of Escher’s more intrigu­ing pieces. The fol­low­ing from the pub­lished arti­cle.

[Prenten­ten­toon­stelling] shows a young man stand­ing in an exhi­bi­tion gallery, view­ing a print of a Mediter­ranean sea­port. As his eyes fol­low the quay­side build­ings shown on the print from left to right and then down, he dis­cov­ers among them the very same gallery in which he is stand­ing. A cir­cu­lar white patch in the mid­dle of the lith­o­graph con­tains Escher’s mono­gram and signature.

What is the math­e­mat­ics behind Prenten­ten­toon­stelling? Is there a more sat­is­fac­tory way of fill­ing in the cen­tral white hole? We shall see that the lith­o­graph can be viewed as drawn on a cer­tain ellip­tic
curve over the field of com­plex num­bers and deduce that an ide­al­ized ver­sion of the pic­ture repeats itself in the mid­dle. More pre­cisely, it con­tains a copy of itself, rotated clock­wise by 157.6255960832… degrees and scaled down by a fac­tor of 22.5836845286….