The Fourth Element

This tutorial clarifies the axiomatic definition of (nu((alpha)), i((beta))) circuit elements via a lookup table dubbed an A-pad, of admissible (nu, i) signals measured via Gedanken probing circuits. The (nu((alpha)), i((beta))) elements are ordered via a complexity metric. Under this metric, the memristor emerges naturally as the fourth element, characterized by a state-dependent Ohm's law. A logical generalization to memristive devices reveals a common fingerprint consisting of a dense continuum of pinched hysteresis loops whose area decreases with the frequency omega and tends to a straight line as omega -> infinity, for all bipolar periodic signals and for all initial conditions. This common fingerprint suggests that the term memristor be used henceforth as a moniker for memristive devices.