From circle packings to constellation patterns

Abstract

We describe a process to convert a circle packing into a dense arrangement of interconnected star motifs. The conversion process is a simple and robust point-joining algorithm, and the resulting family of geometric patterns shares properties with some Islamic star patterns. We demonstrate how some traditional patterns correspond to packings generated from equilateral tilings. We also apply the process to compact packings, which creates balanced versions of some traditional patterns, some new patterns, and visual effects not found in traditional Islamic patterns.