2023/02/25 by Robert A. Hearn, William Kretschmer, Hearn, Robert A. +7 · 1 voice
Physics and Astronomy · #Advanced Mathematical Theories and Applications #cs.CG #math.GR #math.MG
paper · pdf · doi:10.48550/arxiv.2302.12950
openalex publication_date 2023/02/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.