Random Close Packing
The packing of disks in 2D and spheres in 3D has been studied for many centuries now. It's a problem that keeps showing up in many different areas of research because the packing of spherical objects is the simplest model to understand the static structure of more complex packings or assemblies such as liquids, granular media, emulsions, glasses, and living cells.
We typically characterize a packing by its packing fraction and the spatial arrangement of particles. We define the packing fraction to be the percentage of the container's volume occupied by spheres. When spheres are periodically ordered into crystalline arrangements the packing fraction can be relatively large. The most dense 3D packing of spheres is the face centered cubic (fcc) packing, as conjectured by Kepler in 1611, and has a packing fraction near 74%.
There is an entire class of packings that have almost no periodic order in the spatial arrangement of particle positions, and these packings are said to be random packings. Random packings have much lower packing fractions ranging from 55-64%. For a packing with a packing fraction ~55-58% is called a random loose packing and a packing with a packing fraction ~64% is termed a random close packing. For 2D these numbers are much larger, but the concepts and terminology are still the same. Below is a random close packing of binary 2D disks.