I gave a talk on visualizations of modular forms made with Adam Sakareassen at Bridges 2021. This talk goes with our short article. In this talk, I describe the line of ideas going towards producing three dimensional visualizations of modular forms, which I like to call modular terrains. When we first wrote that talk, we were working towards the following video visualization.
We are now working in a few different directions, involving informational visualizations of different forms and different types of forms, as well as purely artistic visualizations.
I’ve recently been very fond of including renderings based on a picture of my wife and I in Iceland (from the beforetimes). This is us as a wallpaper (preserving many of the symmetries) for a particular modular form.
I reused a few images from Painted Modular Terrains, which I made a few months ago.
If you’re interested, you might also like a few previous talks and papers of mine:
- Slides from a talk on Visualizing Modular Forms
- Slides from a talk on computing Maass forms
- Notes behind a talk: visualizing modular forms
- Trace form 3.32.a.a
- phase_mag_plot: a sage package for plotting complex functions
- A paper: Visualizing modular forms
- A paper: Computing classical modular forms
- Bridges paper: Towards flying through modular forms