Last December, I happened to be in Milan just in time for a major Escher exhibition at Palazzo Reale. The Metamorphosis series was my all-time favorite, and I really liked his non-mathematical early works of Italian scenery, but I’d like to share something else in this post.
In “Print Gallery” (1956), Escher left a hole in the center of the lithograph because he did not know how to complete the picture consistently. This is a beautifully done paradox of looking at pictures in a print gallery while being in a picture.
In 2002, number theorist Hendrik Lenstra from Universiteit Leiden found a way to describe the geometry in “Print Gallery” by a complex exponential function. Using conformal mappings, the Leiden group generated a new rendition of “Print Gallery” with the hole filled in.
You can play around with the computer program and zoom in at the project website: http://escherdroste.math.leidenuniv.nl/index.php?menu=im&sub=main&view=2