Formation of Turing patterns of nanoscopic length scale is simulated using molecular dynamics. Based on Fourier spectra of the concentrations of species, we compare stabilities of the structures of different wavelengths and for different intermolecular potentials. Long range attraction is shown to oppose the formation of structures. Our simulations suggest that Turing patterns can be a method of self-organization at a length scale of down to 20 molecular diameters.