Adding to Valerio Talamanca's answer, there was a lecture by Lenstra on Escher's "Paint gallery" at Leiden University (December 12, 2012) which can be viewed [here][1].

Also, my memory says that elliptic curves, rather than complex geometry, played the pivotal role in the explanation (that is why Lenstra explained it).

  [1]: https://www.math-stockholm.se/en/kollokvier/kollokvier-2009-2017/2012/hendrik-lenstra-escher-and-the-droste-effect-1.402774