Random close pack crystal lattices have maximum densities equal to this upper limit. Random close packing does not have a precise geometric definition. It is defined statistically, and results are empirical. A container is randomly filled with objects, and then the container is shaken or tapped until the objects do not compact any further, at this point the packing state is RCP. The definition of packing fraction can be given as: "the volume taken by number of particles in a given space of volume". In other words, packing fraction defines the packing density. It has been shown that the filling fraction increases with
Packing dimension packing dimensions of the set formula_15 are given respectively by: It follows easily that given numbers formula_20, one can choose a sequence formula_4 as above such that the associated (topological) Cantor set formula_15 has Hausdorff dimension formula_23 and packing dimension formula_24. One can consider dimension functions more general than "diameter to the "s"": for any function "h" : [0, +∞) → [0, +∞], let the packing pre-measure of "S" with dimension function "h" be given by and define the packing measure of "S" with dimension function "h" by The function "h" is said to be an exact (packing) dimension function