The Random Packing of Circles in a Plane

A computer simulation study was made of the random packing of unimodal and bimodal circle size distributions under the influence of a weak central force. The random packing fraction of noninteracting circles of uniform diameter was determined to be 0.82. This should be compared with the fraction in hexagonal close packing, 0.907, and in cubical close packing, 0.785. For bimodal distributions with diameter ratios of 1:5 (for which the small circles are just slightly too large to fit into the interstices of hexagonally close-packed large circles) the packing fractions showed a maximum of 0.85 when the number ratios were between 10 and 20. An attempt was made to correlate results obtained on the packing behavior of circles in a plane to those obtained for spheres in space