(A) An illustration of the RRAM array with each memory cell comprising of one filament (sandwiched between two electrodes). In comparison to the surrounding insulator matrix, a number of nano-filaments are formed within the bulk oxide. (B) A basic element of a RRAM cell. Control of the electrical field leads to different resistance states. (C) Localized formation of conductive filaments in a TiO2 thin film. The left shows the conductivity map recorded by CAFM. The right shows the same current mapping in 3D.