Towards Flying through Modular Forms

TL;DR

This paper explores the visualization of modular forms as 3D terrains to reveal their symmetries, aiming to enhance understanding through artistic and computational techniques.

Contribution

It introduces methods for computing and visualizing modular forms as 3D surfaces, facilitating new ways to explore their mathematical properties.

Findings

Created visualizations of modular forms as 3D terrains

Developed techniques for flying around and filming these terrains

Enhanced understanding of modular form symmetries

Abstract

Modular forms are highly self-symmetric functions studied in number theory, with connections to several areas of mathematics. But they are rarely visualized. We discuss ongoing work to compute and visualize modular forms as 3D surfaces and to use these techniques to make videos flying around the peaks and canyons of these "modular terrains." Our goal is to make beautiful visualizations exposing the symmetries of these functions.