Order and disorder in columnar joints

– Columnar joints are three-dimensional fracture networks that form in cooling basalt and several other media. The network organizes itself into ordered, mostly hexagonal columns. The same pattern can be observed on a smaller scale in desiccating starch. We show how surface boundary conditions in the desiccation of starch affect the formation of columnar joints. Under constant drying power conditions, we find a power law dependence of columnar cross-sectional area with depth, while under constant drying rate conditions this coarsening is eventually halted. Discontinuous transitions in pattern scale can be observed under constant external conditions, which may prompt a reinterpretation of similar transitions found in basalt. Starch patterns are statistically similar to those found in basalt, suggesting that mature columnar jointing patterns contain inherent residual disorder, but are statistically scale invariant. Columnar jointing, in which shrinkage fractures arrange themselves to leave behind a pattern of mainly hexagonal pillars, has fascinated scientists and naturalists for centuries [1–3]. The Giant’s Causeway in Northern Ireland and the Devil’s Postpile in California are famous examples. Columnar joints occur in lava flows, sandstone, mud, coal, glass, starch, and ice [3–11], while a 2D variant may cause ice/sand-wedge polygons in permafrost on Earth and Mars [5, 12]. Columnar joints are formed through the self-organization of shrinkage cracks in a three-dimensional material, as either heat or moisture is removed from one surface [6,13,14]. Brittle fracture is initiated by the stress buildup at this surface [14], and the resulting cracks progressively extend, tracking a shrinkage front as it moves into the bulk [15,16]. At any given time, active fractures are confined to a nearly planar layer between the remaining compliant material, and the fully fractured material [15, 16]. The evolution of this quasi-2D polygonal pattern through time is recorded in the depth dependence of the resulting prismatic columns. Often, in geophysical examples, this pattern only becomes apparent when the interior of the formation is exposed by erosion and weathering. As a result, previous geophysical studies of the fracture pattern have been limited to exposed planar surfaces. Columnar jointing is a surprisingly general phenomenon, well known in igneous rocks (both terrestrial [13] and lunar [17]), but also seen in sedimentary [5,10], and metamorphic rocks [5], as well as in manmade and biological materials [4–9]. Examples in basalt and corn starch are shown in Fig. 1. Joints can range in size from micron sized diffusively cooled columns in vitrified, impure, ice [11] to meter sized evaporatively cooled columns in basalt [14].