Great post, though I'm missing a definition of how do they mathematically define segregation. (Checking from the JS code, it seems to be an average over the shapes of the proportion of neighbor shapes which are like them.)
Also, the title confused me a bit as I expected something related to Flatland.
By the way, one of the two people behind this is Vi Hart, which has also made some brilliant videos featuring math, music, and brilliant silliness: https://www.youtube.com/watch?v=4niz8TfY794&list=UUOGeU-1Fig...