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A memory resistor (memristor) is a non-linear passive two-terminal electrical component considered to be the fourth fundamental electrical circuit element, in addition to the original fundamental circuit elements: resistors, capacitors and inductors. Like a resistor, it creates and maintains a safe flow of electrical current across a device, but it can also remember the last charge that was flowing through it. It differs from a regular resistor as it can "remember" charges even when there is no current or voltage present, allowing information storage even when the device is turned off.
The memory resistor started as a theory first presented by Dr. Leon Chua in 1971. It is essentially a two-terminal passive circuit that has a non-linear relationship between the electric charge and the magnetic flux linkage. Though memory resistors still follow the fundamental circuit variables of voltage, current and their time integrals, they have a dynamic function with memory and may be described as some function of net charge, which is not found in the other three fundamental circuit elements.
The memristor is also capable of logic functions which can greatly change the current compartmentalized structure of computing, since this allows the creation of devices that are capable of both processing and storing data in the same space. Currently there is no standard memory resistor, instead, each device implements a particular function wherein the integral of voltage determines the integral of current, and vice versa.
Since memristors are still under development, their future is dependent on determining the best material implementation. Currently IBM, Samsung, HRL, Hewlett Packard and numerous other research labs have been showing interest in the titanium dioxide memristor, but there are quite a few other types of memristors being researched as well.