1. An electrically operated, directly overwritable, multibit, single-cell memory element comprising: a volume of memory material defining a single cell memory element, said memory material characterized by (1) a large dynamic range of electrical resistance values, and (2) the ability to be set at one of a plurality of resistance values within said dynamic range in response to selected electrical input signals so as to provide said single cell with multibit storage capabilities; a pair of spacedly disposed contacts for supplying said electrical input signal to set said memory material to a selected resistance value within said dynamic range; at least a filamentary portion of said single cell memory element being setable, by said selected electrical signal to any resistance value in said dynamic range, regardless of the previous resistance value of said material; and a filamentary portion controlling means disposed between said volume of memory material and at least one of said spacedly disposed contacts, said means defining the size and position of said filamentary portion during electrical formation of the memory element and limiting the size and confining the location of said filamentary portion during use of the memory element, thereby providing for a high current density within said filamentary potion of said single cell memory element upon input of a very low total current electrical signal to said spacedly disposed contacts.