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Atomic Singular Inner Function
This picture, drawn by Elias Wegert, uses colors to show the phase $f/|f|$ of the complex function $$f(z) = \prod_{k=1}^5 \exp\left(\frac{z+\omega^k}{z-\omega^k}\right)$$ where $\omega$ is a nontrivial...
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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...
View ArticlePentagon-Decagon Branched Covering
Two regular pentagons and a regular decagon fit snugly at a point: their interior angles sum to 360°. Despite this, you cannot tile the plane with regular pentagons and decagons. However, there is a...
View ArticleBranched 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...
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