An ordered lattice of lateral InAs quantum dot (QD) molecules is created by self-organized anisotropic strain engineering of an (In,Ga)As/GaAs superlattice (SL) template on GaAs(311)B by molecular-beam epitaxy, constituting a Turing pattern in solid state. The SL template and InAs QD growth conditions, such as the number of SL periods, growth temperatures, amount and composition of deposited (In,Ga)As, and insertion of Al-containing layers, are studied in detail for an optimized QD ordering within and among the InAs QD molecules on the SL template nodes, which is evaluated by atomic force microscopy. The average number of InAs QDs within the molecules is controlled by the thickness of the upper GaAs separation layer on the SL template and t...