Magnetic domains and domain walls in epitaxial Fe3O4(100) elements (rings and wires) are imaged using magnetic force microscopy and photoemission electron microscopy. We show that the interplay between the four-fold magnetocrystalline anisotropy and the shape determines the equilibrium domain structure. Domain walls with a characteristic zig-zag structure are observed in Fe3O4(100) elements initially magnetized along one of the magnetocrystalline hard axes. We attribute the formation of zig-zag domain walls to the competition of the four-fold magnetocrystalline anisotropy, the exchange and dipolar coupling. A direct correlation between the wire width and the spin structure of zig-zag domain walls is found.