Two-Disk Compound Symmetry Groups
Metric Geometry
2025-09-18 v1 Computational Geometry
Group Theory
Abstract
Symmetry is at the heart of much of mathematics, physics, and art. Traditional geometric symmetry groups are defined in terms of isometries of the ambient space of a shape or pattern. If we slightly generalize this notion to allow the isometries to operate on overlapping but non-identical metric spaces, we obtain what we call compound symmetry groups. A natural example is that of the groups generated by discrete rotations of overlapping disks in the plane. Investigation of these groups reveals a new family of fractals, as well as a rich structure that is intriguing both mathematically and artistically. We report on our initial investigations.
Cite
@article{arxiv.2302.12950,
title = {Two-Disk Compound Symmetry Groups},
author = {Robert A. Hearn and William Kretschmer and Tomas Rokicki and Benjamin Streeter and Eric Vergo},
journal= {arXiv preprint arXiv:2302.12950},
year = {2025}
}
Comments
17 pages, 23 figures