The Fractal Beauty of Compound Symmetry Groups

Bob Hearn
Founder & CEO H3 Labs

Stevenson Hall 1300
12:00 PM - 12:50 PM

Symmetry is at the heart of much of mathematics, physics, and art. We generalize the traditional mathematical notion of geometric symmetry by considering groups generated by distinct but overlapping isometries. In particular, we look at the groups generated by discrete rotations of overlapping disks. This yields a rich trove of new, intricate mathematical patterns, containing symmetries that are classically forbidden, as well as a new family of fractals. There is also a connection to quasicrystals, and a surprising connection to puzzles.

I’ll formally introduce compound symmetry groups, show what is known and what remains mysterious about them, and discuss the algorithmic techniques needed to generate the images and probe the dynamics behind the fractal transitions.

This is joint work with Brandon Enright, William Kretschmer, Tomas Rokicki, Ben Streeter, and Eric Vergo.