Methods of fabricating complex three-dimensional structures on patterned substrates and related compositions are provided. The methods involve depositing on the substrate a block copolymer material that is “mismatched” to the substrate pattern, and then ordering the material to form a complex three-dimensional structure. According to various embodiments, the copolymer material mismatches the substrate pattern in that the symmetry and/or length scale of its bulk morphology differs from that of the pattern. When ordered, a balance between the physics that determines the bulk block copolymer morphology and the physics that determines the substrate surface interfacial interactions results in a thermodynamically stable complex three-dimensional film that varies in a direction perpendicular to the substrate and has a morphology that differs from its bulk morphology.