The Fourth Element

This tutorial clarifies the axiomatic definition of (v^(α); i^(β)) circuit elements via a lookup table dubbed an A-pad, of admissible (v; i) signals measured via Gedanken probing circuits. The (v^(α); i^(β)) 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 ω and tends to a straight line as ω ~ ∞, for all bipolar periodic signals and for all initial conditions. This common fingerprint suggests that the term memristor be used hence-forth as a moniker for memristive devices.