Branched Cover from (4 4 3/2) Schwarz Triangle - Greg Egan

Branched Cover from (4 4 3/2) Schwarz Triangle

A Schwarz triangle is a spherical triangle that can be used to generate a tiling of a branched covering of the sphere by repeatedly reflecting this triangle across its edges. Sometimes we get an actual tiling of the sphere, but in general we get a branched covering, because the same point can lie in the interior of several triangles, and there may be branch points at the corners of the triangles.

Weierstrass Elliptic Function (Zoomed Out) - David J. Chudzicki

Weierstrass Elliptic Function

The Weierstrass elliptic function is built up as a sum of terms, one for each point in a lattice in the complex plane. Each term has a pole at one lattice point. The picture here shows the very first term, namely $1/z^2$. That’s why it’s bright in the middle and the colors go twice around the color wheel as you go around. If you continue reading, you’ll see a movie made by David Chudzicki where further terms are added one at a time!