Lead Developer in Research Project Team · 2024
Schottky Visualizations
Stack: StdDraw, Numpy
Motivation
This summer research project focused on a particular set of Mobius Maps known as Schottky Groups. Inspired by the contents of Indra's Pearls our goal was to understand these groups and make them appealing to a broader audience outside of math using the groups stunning visualizations.
Approach
The reflecting property of each map is taken and flipped over its head.
Broadly, the color value of each pixel on the generated visualization is based on the number of times that it can be inverted (using the current group/circle that it's in) until it reaches the fundemental domain.
Features
Both types of Schottky Maps can be though of as circles. The second type is a circle that touches the point at infinity which results in the appearance of a line.
To create certain Schottky Visualizations, apart from the regular circle class I implemented this second circle type so that the inverse logic applies to it as well.