A memristor includes a substrate having a plurality of protrusions, wherein each of the plurality of protrusions extends in a first direction, a first electrode provided over at least one of the plurality of protrusions, wherein the first electrode conforms to the shape of the at least one protrusion such that the first electrode has a crest, a switching material positioned upon the first electrode; and a second electrode positioned upon the switching material such that a portion of the second electrode is substantially in line with the crest of the first electrode along the first direction, wherein an active region in the switching material is operable to be formed between the crest of the first electrode and the portion of the second electrode that is substantially in line with the crest of the first electrode.