Iron oxide films epitaxially grown on close-packed metal single crystal substrates exhibit nearly-perfect structural order, high catalytic activity (FeO) and room-temperature magnetism (Fe₃O₄). However, the morphology of the films, especially in the ultrathin regime, can be significantly influenced by the crystalline structure of the used support. This work reports an ultra-high vacuum (UHV) low energy electron/synchrotron light-based X-ray photoemission electron microscopy (LEEM/XPEEM) and electron diffraction (µLEED) study of the growth of FeO and Fe₃O₄ on two closed-packed metal single crystal surfaces: Pt(111) and Ru(0001). The results reveal the influence of the mutual orientation of adjacent substrate terraces on the morphology of iron oxide films epitaxially grown on top of them. On fcc Pt(111), which has the same mutual orientation of adjacent monoatomic terraces, FeO(111) grows with the same in-plane orientation on all substrate terraces. For Fe₃O₄(111), one or two orientations are observed depending on the growth conditions. On hcp Ru(0001), the adjacent terraces of which are ‘rotated’ by 180° with respect to each other, the in-plane orientation of initial FeO(111) and Fe₃O₄(111) crystallites is determined by the orientation of the substrate terrace on which they nucleated. The adaptation of three-fold symmetric iron oxides to three-fold symmetric substrate terraces leads to natural structuring of iron oxide films, i.e., the formation of patch-like magnetite layers on Pt(111) and stripe-like FeO and Fe₃O₄ structures on Ru(0001).