Spontaneous Patterns in Disk Packings

Boris D. Lubachevsky, Ron L. Graham and Frank H. Stillinger
Bridges: Mathematical Connections in Art, Music, and Science (1998)
Pages 181–194


Using a computational procedure that imitates tightening of an assembly of billiard balls, we have generated a number of packings of n equal and non-equal disks in regions of various shapes for n in the range 10 to 10,000. Our experiments revealed various geometric patterns and regular features, including polycrystalline textures with "rattlers" typically trapped along the grain boundaries. We also observed series of packings with similar patterns for n taking on increasing sequences of values, n = n(I), n(2), ... n(k), ....