Weak van der Waals interactions between 2D materials layers do not impose limitations on integrating highly disparate materials such as graphene, hexagonal boron nitride and many others. This is both a blessing, allowing the realization of many more configurations, and a curse from a modeling perspective due to the loss of periodicity. Unusual geometries appear at the atomic-scale, such as lattice mismatches, twist angles and Moire patterns, providing new challenges for our fundamental understanding. Dynamic and macroscopic properties of such aperiodic condensed matter systems can be formulated in the framework of C*-algebras introduced by Bellissard and his co-authors. I will present efforts towards an effective computational implementation of these abstract objects. Indeed, direct finite-volume approximants for tight-binding models of incommensurate 2D Moiré patterns converge too slowly and a different approach is required.