Hierarchical crack pattern as formed by successive domain divisions. I. Temporal and geometrical hierarchy

Crack patterns, as they can be observed in the glaze of ceramics or in desiccated mud layers, are formed by successive fractures and divide the two-dimensional plane into distinct domains. On the basis of experimental observation, we develop a description of the geometrical structure of these hierarchical networks. In particular, we show that the essential feature of such a structure can be represented by a genealogical tree of successive domain divisions. This approach allows for a detailed discussion of the relationship between the formation process and the geometric result. We show that--with some restraints--it is possible to reconstruct the history of the system from the geometry of the final pattern.