Patterns are everywhere in the universe. Magnets, ball bearings, soap bubbles, and even molecules all tend to arrange themselves in similar patterns. But why? Identifying and explaining these patterns is the business of physics.

If you’ve ever played with small magnets—and I bet you have!— you know that when the north and south poles of two magnets are brought together, they attract. Flip one of the magnets around, and the two north poles (or two south poles) will push each other away. As the magnets move farther apart, the force between them weakens. With more than two magnets, this seemingly simple rule can produce surprisingly intricate patterns, and accounting for all the forces gets more and more complicated.

Imagine a single mobile magnet surrounded by a ring of fixed magnets. The magnets in the ring will push and pull the central magnet until it comes to rest at a point where all the forces are balanced. And what if there are multiple free magnets? To answer this question, we stuck some magnets to the walls of a container, added water to the container, and placed other magnets inside small “buckets” so they could float on the water (Fig. 1). Then we let the floating magnets move around until the repulsive forces on each one were balanced. The equilibrium positions of the magnets depend on the interaction of their magnetic fields, as shown in Fig. 2. (You can try something similar with specially prepared Legos: see Froot Loops, Legos, and Self-Assembly.)

These floating magnets are exhibiting a phenomenon called self-assembly (see From Nanowaffles to Nanostructures!). But self-assembly doesn’t only occur with magnets—all objects tend to arrange themselves so the forces acting on them are balanced. In Fig. 3, for example, notice how the configuration of metal ball bearings changes as the boundary confining them is gradually squished from a circle into a long, narrow oval called an ellipse.

When we tried this same experiment with bubbles and then with magnets, we found that all three—ball bearings, bubbles, and magnets—self-assembled in similar ways (Fig. 4). Even more remarkably, stretching or flattening the container produced similar changes in the arrangement of all three! At first, it seems surprising that such dissimilar objects behave in similar ways. Ball bearings, bubbles, and magnets have one very important thing in common, however: they all push each other away.

To see if our results could be generalized even further, we performed computer simulations of interacting particles, with the only rule that the repulsion between particles decreases with the distance between them. Amazingly, we found the same arrangements for all the different systems we tested. The patterns are universal! This result is exciting not only because physicists love patterns (and we really, really do), but because it will enable us to control the self-assembly process in a wide range of situations simply by varying the number of objects and changing the shape of their container.

This technique may eventually enable us to engineer specific patterns that are desirable for particular applications like targeted drug delivery or quantum computing. But first, we need to find out if the universality we observed in two dimensions still holds true in three dimensions (for example, when the container is a sphere instead of a circle). We don’t know yet—but we do know that this subject is full of surprises!

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