Escher's most mathematically interesting piece

The Print Gallery, and the tour of complex analysis it invites.

This may be one of the most involved videos I’ve ever done for the channel, but it was a blast to produce. M.C. Escher has countless pieces that are fascinating for some mathematical reason, but his Print Gallery may top them all (I would say in close contention with his Circle Limit series).

Aside from analyzing the piece, offering both an artistic description based on how Escher approached and a more mathematical one based on work by the mathematicians de Smit and Lenstra, I wanted to use this as a motivation to introduce certain ideas from complex analysis, such as conformal maps and the complex logarithm. Enjoy!