Comparing dragonfly wings to jars of marbles through the lens of hyperuniformity

When we look at the world around us, we see both organized (also called ordered) and disorganized (also called disordered) arrangements of things. Carefully-tiled floors and brick walls have organized and repeating patterns, but the stars in the sky and the trees in a forest look like they're arranged in a disordered way. We also see objects, like jars of marbles and the lacy wings of insects, that lie between ordered and disordered extremes. Although the marbles in a jar don't sit on a regular grid like carefully-arranged tiles, the collection of marbles does have some consistent features, such as the typical size and spacing between them. However, the positions of the marbles are much less random than the positions of the stars in the sky. To help understand and classify these patterns, mathematicians and physicists use the term hyperuniform to help them describe the situations of being perfectly organized or being disorganized in an organized way. In this article, we discuss various fascinating properties of hyperuniform patterns. We explore where they occur in the natural world and how engineers are using them to build new structures.