Statistics of contractive cracking patterns

The statistics of convective soil patterns are analyzed using statistical crystallography. An underlying hierarchy of order is found to span four orders of magnitude in characteristic pattern length. Strict mathematical requirements determine the two-dimensional (2D) topology, such that random partitioning of space yields a predictable statistical geometry for polygons. For all lengths, Aboav's and Lewis's laws are verified; this result is consistent both with the need to fill 2D space and most significantly with energy carried not by the patterns' interior, but by the boundaries. Together, this suggests a common mechanism of formation for both micro- and macro-freezing patterns.