Sequential fragmentation: the origin of columnar quasihexagonal patterns.

We present a model that explains the origin and predicts the statistical properties of columnar quasihexagonal crack patterns, as observed in the columnar jointing of basaltic lava flows. Induced by temperature gradients during cooling, irregular fractures appear at the surface of the material. At later times fractures penetrate into the material, and tend to form polygonal patterns. We show that this ordering can be described as a tendency to minimize an energy functional. Atomistic simulations confirm this interpretation. Numerical simulations based on a phenomenological implementation of this principle generate patterns that have remarkably good statistical agreement with real ones.