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Bibliographic Details
Main Authors: Hearn, Robert A., Kretschmer, William, Rokicki, Tomas, Streeter, Benjamin, Vergo, Eric
Format: Preprint
Published: 2023
Subjects:
Online Access:https://arxiv.org/abs/2302.12950
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Table of Contents:
  • 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.