Looping Animations Using the Modular Flow and Elliptic Functions

TL;DR

This paper introduces a novel method for creating seamless looping animations by leveraging the mathematical properties of modular flow and elliptic functions, visualized through domain coloring techniques.

Contribution

It presents a new approach combining modular flow and elliptic functions to generate visually appealing, mathematically grounded looping animations.

Findings

Generated animations exhibit continuous looping without visible seams.

The method effectively visualizes complex elliptic functions through domain coloring.

The approach offers a mathematically elegant way to produce artistic animations.

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.