Molecular devices are capable of performing a number of functions from mechanical motion to simple computation. Their utility is somewhat limited, however, by difficulties associated with coupling them with either each other or with interfaces such as electrodes. Self-assembly of coupled molecular devices provides an option for the construction of larger entities that can more easily integrate with existing technologies. Here we demonstrate that ordered organometallic arrays can be formed spontaneously by reaction of precursor molecular rotor molecules with a metal surface. Scanning tunnelling microscopy enables individual rotors in the arrays to be switched and the resultant switches in neighbouring rotors imaged. The structure and dimensions of the ordered molecular rotor arrays dictate the correlated switching properties of the internal submolecular rotor units. Our results indicate that self-assembly of two-dimensional rotor crystals produces systems with correlated dynamics that would not have been predicted a priori.