A drying puddle of mud becomes covered with cracks, like an old painting with craquelure. At first the cracks meet at nearly right angles, forming a rough grid. But if the mud is wetted again and allowed to dry, the pattern changes: cracks begin to meet in threes, at an angle of 120 degrees, like a honeycomb.

Why this happens remained a mystery for a long time. Scientists at Osaka University built a computer model that reproduces cycles of drying and wetting. In the model, the paste is a thin layer that shrinks as it dries, and the cracks are zones where the material is weakened. After each wetting, the cracks "heal," but they leave scars: places where the material is no longer as strong.

After the first cycle, 90 degrees dominates the distribution of angles: these are T-shaped intersections. But with each subsequent cycle, the share of angles near 120 degrees grows, that is, Y-shaped intersections. The deviation from 120 degrees decays exponentially with a characteristic time of 2.85 cycles. Experiments with coffee paste give a similar time, about four cycles.

Cracks behave like rivers that straighten their channels with every flood. A river does not flow along a winding path if it can carve a shorter one. So it is with cracks: a Y-shaped intersection at 120 degrees gives a smaller total length than a T-shaped one at 90 degrees. The energy of the cracks in the model decays exponentially with a characteristic time of 3.17 cycles, almost the same as the angle.

This discovery helps explain why drying soils, ceramics, and other materials that alternately get wet and dry develop cracks. In agriculture, predicting soil cracking matters for irrigation, and in construction, for the durability of coatings. The model can be improved by describing the scars from past cracks more realistically, but even now it shows that cracks remember their history and learn to be shorter with each cycle.