Resistive switching of thermally treated rutile single crystals with (110) orientation is studied. A heat treatment procedure is developed that involves reduction and oxidation steps and allows to induce low resistance states in switchable regions at the surface by low-voltage electrical stimulation with the conducting tip of an atomic force microscope. This way, it is possible to electrically imprint quasi-homogeneous switchable regions over several square micrometers. These regions are identified to consist of nanofilaments crossing the surface with a density of around 10(12) cm(,)(-2) much higher in density than observed for single crystals so far. Experimental evidence is given that these nanofilaments are not related to inherent structural imperfections such as dislocations, but may originate from the linear agglomeration of oxygen vacancies as predicted by theory. Ab initio calculations and electrical simulations are performed to analyze the filamentary structures and their network in the effort to explain the observed filamentary switching of heat-treated single-crystalline TiO2.