Laterally ordered InGaAs quantum dot (QD) arrays, InAs QD molecules, and single InAs QDs in a spot-like periodic arrangement are created by self-organized anisotropic strain engineering of InGaAs/GaAs superlattice (SL) templates on planar GaAs (311)B substrates in molecular beam epitaxy. On shallow- and deep-patterned substrates the respectively generated steps and facets guide the self-organization process during SL template formation to create more complex ordering such as periodic stripes, depending on pattern design. Here we demonstrate for patterns such as shallow- and deepetched round holes and deep-etched zigzag mesas that the self-organized periodic arrangement of QD molecules and single QDs is spatially locked to the pattern sidewa...