Inapplied mathematics, aGilbert tessellation[1] orrandom crack network[2] is a mathematical model for the formation ofmudcracks, needle-likecrystals, and similar structures. It is named afterEdgar Gilbert, who studied this model in 1967.[3]
In Gilbert's model, cracks begin to form at a set of points randomly spread throughout the plane according to aPoisson distribution. Then, each crack spreads in two opposite directions along a line through the initiation point, with the slope of the line chosen uniformly at random. The cracks continue spreading at uniform speed until they reach another crack, at which point they stop, forming a T-junction. The result is atessellation of the plane by irregularconvex polygons.
A variant of the model that has also been studied restricts the orientations of the cracks to be axis-parallel, resulting in a random tessellation of the plane byrectangles.[4][5]
Gray et al. (1976) write that, in comparison to alternative models in which cracks may cross each other or in which cracks are formed one at a time rather than simultaneously, "most mudcrack patterns in nature topologically resemble" the Gilbert model.
