Taxicabs And Invisible Rectangles

I had a blast doing my senior project during undergrad. I thought the problem led to a very elegant way of visualizing the whole thing, and it built incrementally in a way I loved. So I made it into a game!  My submission for 3Blue1Brown's The Summer of Math Exposition.

(Please note that only the zip file seems to work across all computers, and is the recommended file to download)