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    $\begingroup$ It's a good way to get the OP started. An extension would be to allow for wiggling the locations. One could also treat it as like an electromagnetics problem, for instance — think of the spheres as all having unit charge and reposition the spheres just as they would when another charged sphere is added to the existing bunch, subject to the constraint that none leave the box. $\endgroup$ Commented Oct 12, 2012 at 3:36
  • $\begingroup$ The alternate type approach is to randomly place spheres so that each exactly touches three others. Much tougher to implement but it will get you ultimately to higher density (50+%). $\endgroup$ Commented Oct 12, 2012 at 4:01
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    $\begingroup$ A relatively simple scheme could be to select a random sphere in the list, then creating a new sphere that touches it in a random direction. This got me to 1856 spheres in a few minutes. $\endgroup$ Commented Oct 12, 2012 at 4:54
  • $\begingroup$ Why is the standing assumption that the metric space is Euclidean (L2-norm)? $\endgroup$ Commented Oct 12, 2012 at 6:22