  We examine emergent properties of 2D supramolecular networks, using
enumeration of configurations formed by interacting dominoes on square lattices
as a simple model system. Possible ground states are identified using a convex
hull construction in the interaction parameters for nearest-neighbour bonds. We
demonstrate how this construction can be used to design interaction parameters
which lead to networks with specific properties, including chirality and highly
degenerate ground states. We then introduce kinetics as simple local
rearrangements. By partitioning the configuration space into smaller sets which
satisfy different topological constraints, we can design configurations which
are kinetically trapped. By considering heat capacity curves along directions
through the convex hull, we also demonstrate design of interacting domino
configurations to create tilings robust against temperature induced phase
transitions. We discuss extension of this design construction to more complex
molecular shapes.
