Two-Disk Compound Symmetry Groups

Year: 2023 Authors: Robert A. Hearn; William Kretschmer; Tomas Rokicki; Benjamin Streeter; Eric Vergo

Core claim

Overlapping disk rotations generalize symmetry groups and yield a threshold between finite and infinite behavior, with fractal patterns appearing at critical radii.

Topics

compound symmetry groups, two-disk systems, critical radius, fractals

Domains

group theory, dynamical systems, piecewise isometries, crystallographic restriction, mathematical art, pattern design, circle puzzles, visual symmetry

Methods

theoretical analysis, group characterization, orbit growth reasoning, examples and figures

Media

overlapping disks, fractal portraits, circle puzzles, rotational generators

Source status

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