Order Through Chaos

A maximally dense packing of spheres with high entropy. 

Curiously, researchers found that chaotic arrangements of spheres – or the ones with the most entropy – were also the most symmetrical and ordered. In fact, when the researchers tried packing billiard-ball-like spheres in a number of ways, the most chaotic ones were consistently the most symmetrical.

Related Abstract

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Reporters and Editors

Journalists wishing to reproduce this image for news stories about related research should include the following image credit: Adam B. Hopkins, Frank H. Stillinger, and Salvatore Torquato (Princeton University).