Atomic Singular Inner Function with Atoms at Fifth Roots of Unity - Elias Wegert, www.visual.wegert.com

Atomic Singular Inner Function

This picture, drawn by Elias Wegert, uses colors to show the phase f/|f| of the complex function

f(z)=k=15exp(z+ωkzωk)

where ω is a nontrivial fifth root of unity. This is an ‘atomic singular inner function’. To understand what that means, it helps to start with some complex analysis.

Catacaustic of a Cardioid - Greg Egan

Catacaustic of a Cardioid

This image, drawn by Greg Egan, shows a cardioid and its catacaustic. The cardioid is a heart-shaped curve traced by a point on the perimeter of a circle that is rolling around a fixed circle of the same radius. The catacaustic of a curve in the plane is the envelope of rays emitted from some…