This is very cool! I would love the ability to scribble arbitrary smooth curves (like a little right hand, or a comma, something asymmetric to highlight the symmetries in play) and see how they are repeated.

on the concept of Wallpaper Groups: https://en.wikipedia.org/wiki/Wallpaper_group

Very cool!

If you're just learning about the Wallpaper Groups from this and feel like you've seen them before, it is probably from the work of MC Escher [0].

If you want a great recent survey, an episode of (the inimitable and now restarted) In Our Time from last month goes into the friendship / mutual influence of Escher and Coxeter. [1]

[0] https://eschermath.org/wiki/Regular_Division_of_the_Plane_Dr...

[1] https://www.bbc.com/audio/play/m002v19c