Looping Animations Using the Modular Flow and Elliptic Functions

TL;DR

An approach to generating looping animations using the modular flow and elliptic functions and meromorphic, doubly-periodic functions is described.

Abstract

This paper describes an approach to generating looping animations using the modular flow and elliptic functions. The modular flow is a flow on lattices with many periodic orbits, and elliptic functions are meromorphic, doubly-periodic functions which can be visualized using domain coloring.

Figures (2)

• Figure 4: The animation Modular Flowmodularflow.
• Figure 9: Domain coloring animation of the Weierstrass functions $\sigma_{t \cdot \Lambda}$.