Chaotic crystallography: how the physics of information reveals structural order in materials

•Review information-theoretic and computation-theoretic measures that describe structure in disordered materials.•Extends view of exact periodic crystalline order of group theory to include partial symmetries using semi-group theory.•Opens up the possibility of automated search for useful physical properties in disordered materials.

We review recent progress in applying information-theoretic and computation-theoretic measures to describe material structure that transcends previous methods based on exact geometric symmetries. We discuss the necessary theoretical background for this new toolset and show how the new techniques detect and describe novel material properties. We discuss how the approach relates to well known crystallographic practice and examine how it provides novel interpretations of familiar structures. Throughout, we concentrate on disordered materials that, while important, have received less attention both theoretically and experimentally than those with either periodic or aperiodic order.