1. A multilayer memristive device comprising: a first electrode; a second electrode; a first memristive region; a second memristive region, said first memristive region and said second memristive region being created by directional ion implantation of dopants into a memristive matrix; said first memristive region and said second memristive region being interposed between said first electrode and said second electrode; and mobile dopants; said mobile dopants moving within said first memristive region and said second memristive region in response to an applied electrical field.