This is something I put together for my Elective class “Journey to the 4th Dimension” to explore 2D manifolds: Cylinder, Möbius Loop, Klein Bottle, Torus, and Projective Plane. You can play basic games like tic-tac-toe and word search on these manifolds and see how, while they are locally 2-dimensional, things get weird and non-orientable once the manifolds start twisting!
I first became interested in these shapes when I visited Cliff Stoll at his home in Berkeley and we geeked out on Klein Bottles (and his underground Klein Bottle warehouse). After that, I discovered the smartphone app Torus Games by Jeff Weeks. I wanted to play these games in the elective, but they were only available as an app which had to be downloaded – not easy to do on school devices or students’ personal devices with parental controls. So I decided to try vibe coding- something I had only experimented with a little bit. Since Weeks’ code base is open source, I figured this was an appropriate use-case.
The result is this page, which I hosted on my github. Have fun!