When a thin layer of clay dries, it cracks. The cracks form a network — polygons subdividing the surface. The pattern looks random, but the junctions encode the order of formation.
The first crack in a drying film runs uninterrupted across the surface, relieving stress along its length and perpendicular to its orientation. The second crack forms in the residual stress field left by the first. It propagates until it meets the first crack, where it terminates at approximately ninety degrees — a T-junction. The geometry is dictated by physics: the existing crack has already relieved stress in its neighborhood, so the approaching crack curves to meet it perpendicularly, joining where the stress gradient is steepest.
Each subsequent crack does the same: propagates through stressed material and terminates at an existing crack. The result is a hierarchical network. Older cracks are longer and uninterrupted. Younger cracks are shorter fragments bounded by older ones. The first-order cracks — the founders of the network — have mean relative lengths of 0.12. By the third order, the fragments average 0.58. The founders span more of the domain; the followers fill in the gaps.
Tarasevich, Eserkepov, and Vodolazskaya capture this hierarchy with a recursive Voronoi algorithm. Place seeds, partition the domain, then recursively partition each cell again. Each level of recursion corresponds to a generation of cracks. The resulting networks reproduce the junction-angle distributions, cell-shape statistics, and topological features of real desiccation patterns — pentagons most common, then hexagons, then quadrangles.
The T-junction is the signature of sequential formation. When two cracks meet at ninety degrees with one terminating and the other continuing, you know which came first — the continuous one is older. The topology records time. Read the network backward from its junctions and you reconstruct the order of formation, centuries after the last drop of water evaporated.
But repeat the wetting-drying cycle and the junctions change. T-junctions evolve toward Y-junctions — three cracks meeting at approximately 120 degrees, none dominant. The hierarchical record erases. The network converges on a hexagonal tiling, which is the minimum-energy configuration. The first few cycles produce the most dramatic reorganization; by the third or fourth cycle, the pattern stabilizes. The equilibrium network carries no information about which crack came first because no crack came first — they formed simultaneously.
Two geometries of junction, two modes of formation, two relationships with time. T-junctions record history. Y-junctions erase it. A network of T-junctions is a diary. A network of Y-junctions is a crystal. The same material, the same forces, the same scale — but the protocol of formation (one drying event versus many) determines whether the pattern remembers or forgets.
The crack pattern is not just a consequence of stress. It is a document. The angles at the junctions are a timestamp. The connectivity is a narrative of which regions failed first and which held on longest. When you look at cracked earth, you are reading the mechanical autobiography of a surface.