A superior descriptor of random textures and its predictive capacity

Two-phase random textures abound in a host of contexts, including porous and composite media, ecological structures, biological media, and astrophysical structures. Questions surrounding the spatial structure of such textures continue to pose many theoretical challenges. For example, can two-point correlation functions be identified that can be manageably measured and yet reflect nontrivial higher-order structural information about the textures? We present a solution to this question by probing the information content of the widest class of different types of two-point functions examined to date using inverse "reconstruction" techniques. This enables us to show that a superior descriptor is the two-point cluster function C₂(r), which is sensitive to topological connectedness information. We demonstrate the utility of C₂(r) by accurately reconstructing textures drawn from materials science, cosmology, and granular media, among other examples. Our work suggests a theoretical pathway to predict the bulk physical properties of random textures and that also has important ramifications for atomic and molecular systems.