A magnetic film divided into tiny arrow-shaped cells behaves like a crowd in a square. While it's cold, all arrows point in the same direction — perfect order. Heat the film, and the arrows start darting around like pedestrians who have lost their purpose. Somewhere between these extremes, there is a moment when the system stops being uniform but hasn't yet dissolved into random noise.

Physicists took such a model — the two-dimensional Ising lattice, known for its abrupt change at a critical temperature. They captured snapshots of the lattice states at different temperatures and compressed them like ordinary pictures on a phone. Compression reveals how much regularity is in an image: a perfectly uniform pattern packs into a tiny file, while white noise barely compresses. To account for both order and chaos, the researchers compared each state with its shuffled versions — one sorted by colors and one completely mixed.

They built a complexity measure as the product of two numbers: how far the system is from perfect order and how far from complete disorder. A plot of this measure against temperature showed a sharp peak exactly at the phase transition point. This means that structural complexity is a reliable beacon of the critical state, which can be found without complex formulas, simply by compressing data.

This approach is useful where analytical solutions are unavailable: in biology, climate, and social networks. Everywhere a system churns on the edge of order and chaos, data compression can hint when to expect abrupt changes.