The Best Packing of M&Ms

The best packing of M&Ms, filling more than 77% of available volume, has been achieved in a computer simulation performed at Princeton. Actually the new results apply to any ellipsoid object, such as M&M candy, fish eggs, or watermelons.

The modern understanding of dense packing might be said to start in 1611, when Johannes Kepler suggested that the most efficient packing of spheres in a container occurred when the spheres were placed in a face-centered cubic arrangement---the way a grocer stacks oranges. "Kepler's conjecture" was proved in 1998 and the filling factor was worked out to be about 74%. Unlike spheres, which still look the same after you rotate them, ellipsoids' oblateness (they are squashed or stretched in at least one direction) give them orientational degrees of freedom that spheres don't have. Consequentially, ellipsoids can be packed more efficiently than spheres. Depending on the aspect ratio of the ellipsoid, the packing density can be anywhere between 74% and 77%.

The Princeton research (contact Salvatore Torquato, 609-258-3341, torquato@electron.princeton.edu) has a number of practical implications: it shows that glassy states of matter, in which molecules lie in a disordered arrangement, can have densities almost as high as for crystals; it suggests that because of a high contact number (in the high-density packings ellipsoids can touch 14 of their neighbors) stronger ceramics can be designed; and it encourages researchers to investigate the effect of ellipsoidal shape on evolutionary optimization in fish eggs. (Donev et al., Physical Review Letters, upcoming article.)