Full article: From circle packings to constellation patterns

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. Keywords: Systems of tangent circles have been used to give structure to ornamental designs in many cultures. Some patterns are derived from the natural world. Buddhist symbols in Japan include many different packings of equal circles in a circular frame (Tarnai & Miyazaki, Citation 2003). They imitate the distribution of seeds in the fruit of the lotus plant – the seed pod resembles a shower head with an array of holes in its

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. Keywords: Systems of tangent ci