Circles reflected through circles become intricate necklaces. Quiet openings hold the composition while tiny pearls collect around their edges.
Circle inversion · Schottky reflection groups
A finite circle-inversion construction related to Kleinian limit sets. Each circle is inverted in every generator except the one just used. Disjoint generating circles keep the reflections bounded; sub-pixel circles are omitted. The five construction circles are omitted to reveal the necklaces between them. The filled discs are an artistic treatment of the construction, not the limit set itself.
Behind the mathematics
Kleinian groups
German mathematician whose Erlangen programme recast geometry as the study of symmetry groups. The Kleinian groups, built from reflections in circles, are named after him; their limit sets are the lace of fractal pearls.
Schottky groups of paired circles
German mathematician who introduced the groups named after him, made by pairing off circles that do not touch; their repeated images nest into necklaces of ever smaller circles.
