Why cracked dry mud and paint form polygonal networks

Partly settled. Some of it is understood, some is still argued about.

Desiccating mud has been observed to crack into polygons since antiquity, but a quantitative physics treatment began with Groisman & Kaplan's 1994 tabletop experiments on colloidal suspensions. The hard part is that fracture nucleates from random defects yet self-organizes into a statistically regular polygonal network, with crack spacing scaling with layer thickness. Goehring, Clegg, Routh and coworkers showed experimentally that repeated wetting-drying cycles shift the pattern from 90-degree T-junctions toward the more efficient 120-degree honeycomb-like junctions, and derived scaling laws relating crack gap to layer thickness. Full quantitative prediction of crack statistics from material properties remains an active soft-matter research topic, so this is best described as partially, not fully, solved.

A layer of ordinary mud spontaneously computes something close to the most efficient possible tiling of a cracked surface, using nothing but stress and time.

Explanations that circulated

• Cracks are purely random with no predictable geometry
• The 90-degree vs 120-degree T-junction angles are fixed material constants rather than depending on drying history/repeated wetting cycles

References

• Evolution of mud-crack patterns during repeated drying cycles, L. Goehring, R. Conroy, A. Akhter, S. S. Clegg, A. F. Routh, Soft Matter, 2010
• Universal Scaling of Polygonal Desiccation Crack Patterns, various (crack-pattern scaling review), arXiv, 2018