The Riemann surface of arctan

Riemann surfacesWikipedia. We all know and love them.

The complex logarithmen.wikipedia.org is easy enough, but until now I was in the dark about how the complex arctangent “looked”.

Until I found this fascinating paperwww.futuretg.com and was enlightened. I plotted it in Mathematica here:

Tonight I will dream of infinite blue staircases 😴.