Editing Sphere packing (section)

== Irregular packing ==
{{main|Random close pack}}
If we attempt to build a densely packed collection of spheres, we will be tempted to always place the next sphere in a hollow between three packed spheres. If five spheres are assembled in this way, they will be consistent with one of the regularly packed arrangements described above. However, the sixth sphere placed in this way will render the structure inconsistent with any regular arrangement. This results in the possibility of a ''random close packing'' of spheres which is stable against compression.<ref>{{cite journal|title=Random thoughts|first=Paul|last=Chaikin|date=June 2007|journal=Physics Today|page=8|issn=0031-9228|publisher=American Institute of Physics|volume=60|issue=6|doi=10.1063/1.2754580|bibcode = 2007PhT....60f...8C }}</ref> Vibration of a random loose packing can result in the arrangement of spherical particles into regular packings, a process known as [[Granular material#Pattern formation|granular crystallisation]]. Such processes depend on the geometry of the container holding the spherical grains.<ref name=grancrys/>

When spheres are randomly added to a container and then compressed, they will generally form what is known as an "irregular" or "jammed" packing configuration when they can be compressed no more. This irregular packing will generally have a density of about 64%. Recent research predicts analytically that it cannot exceed a density limit of 63.4%<ref name="nature">{{cite journal |last1=Song |first1=C. |last2=Wang |first2=P. |last3=Makse |first3=H. A. |date=29 May 2008 |title=A phase diagram for jammed matter |journal=[[Nature (journal)|Nature]] |volume=453 |pages=629–632 |doi=10.1038/nature06981 |pmid=18509438 |issue=7195 |bibcode = 2008Natur.453..629S |arxiv = 0808.2196 |s2cid=4420652 }}</ref> This situation is unlike the case of one or two dimensions, where compressing a collection of 1-dimensional or 2-dimensional spheres (that is, line segments or circles) will yield a regular packing.