Working out the Stern-Brocot tree using modular arithmetic leads to some finite shapes because after a while the calculation repeats itself. For example, using

Working out the Stern-Brocot tree using modular arithmetic leads to some finite shapes because after a while the calculation repeats itself. For example, using mod 5 you get a dodecahedron! These things are called modular curves (iirc.) It's a little bit tricky to figure this out, one hint is that every fraction has two names a/b and -a/-b. In modular arithmetic this is important, eg. 2/3 == -2/-3 == 3/2. So every node of the tree has two labels. (Warning: I may not be explaining this very well.) Once you get to mod 7 you get a three-holed donut shape, called the Klein quartic.