Ordered groups of InAs quantum dots (QDs), lateral QD molecules, are created by self-organized anisotropic strain engineering of a (In,Ga)As/GaAs superlattice (SL) template on GaAs (311)B by molecular beam epitaxy (MBE). During stacking the SL template self-organizes into a highly ordered two-dimensional (In,Ga)As and, thus, strain field modulation on a mesoscopic length scale, constituting a Turing pattern in solid state. InAs QDs preferentially grow on top of the SL template nodes due to local strain recognition, forming a lattice of separated groups of closely spaced ordered QDs. The SL template and InAs QD growth conditions like 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 optimized QD ordering within and among the InAs QD molecules on the SL template nodes, which is evaluated by atomic force microscopy (AFM). 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 the (In,Ga)As growth temperature in the SL. The strain correlated growth in SL template formation and QD ordering is directly confirmed by high-resolution X-ray diffraction (XRD). Ordered arrays of single InAs QDs on the SL template nodes are realized for elevated SL template and InAs QD growth temperatures together with the insertion of a second InAs QD layer. The InAs QD molecules exhibit strong photoluminescence (PL) emission up to room temperature. Temperature dependent PL measurements exhibit an unusual behavior of the full-width at half-maximum, indicating carrier redistribution solely within the QD molecules.