New Packing Algorithm Fits All Shapes and Sizes Most Effectively

Stacking for example Rubik cubes in a storage box is a fairly easy task. They are all the same size, and can be neatly stacked on top of each other in established patterns. But when it comes to fitting as many gumballs in a single vending machine bowl, things get a little complicated. Establishing the most effective way of storing objects of various shapes and sizes into existing packages has proven to be elusive for mathematicians developing models to address this issue until now.

Experts at the New York University Materials Research Science and Engineering Center report in the latest issue of the respected journal Nature that they managed to devise such an algorithm, which addresses a fairly intuitive, but difficult to prove theoretically, problem. Physicists at the university have determined that the efficiency with which the space in a bowl is used by the gumballs inside is given by the number of neighboring balls each of them touches. Less neighbors means more empty space around it, and implicitly the fact that less gumballs get to go in.

The new mathematical model that maximizes such scenarios – that deal with arranging misc 3D objects of various shapes and sizes with the utmost efficiency – was developed by researchers Maxime Clusel, Eric Corwin and Alex Siemens, who were led by NYU Physics Professor Jasna Brujic. Their work was funded by the National Science Foundation (NSF). “We have discovered a simple organizing principle for particulate packing that predicts our experimental findings,” the team leader explains.

“Bigger particles pack with more neighbors, while smaller particles have on average fewer neighbors. By combining this simple insight with probabilistic mathematics we created an accurate model demonstrating how this organizing rule gives rise to packings where particles have a wide range or distribution of contacts, neighbors and local densities,” Corwin, who is a postdoctoral research fellow at the university, adds.

“We were surprised to find that such a simple model, based on physical intuition alone, could capture the properties of a complex packing of droplets in an emulsion,” Brujic concludes.