maximally random jammed | random ellipsoid packing | random sphere packing

The concept of "random close packing" was shown by Torquato et al. (2000) to be mathematically ill-defined idea that is better replaced by the notion of "maximally random jammed." Random close packing of circles in two dimensions has a theoretical packing density of 0.886441. Random close packing of spheres in three dimensions gives a packing density of only η≈0.64 (Bernal and Mason 1960, Jaeger and Nagel 1992, Zaccone 2022), significantly smaller than the optimal packing density for cubic or hexagonal close packing of 0.74048.

cubic close packing | ellipsoid packing | hexagonal close packing | sphere packing