A memristor is a two-terminal nanodevice whose resistance depends on the history of the current that has flowed through it — it "remembers" its past. Inside a thin metal-oxide film, a positive voltage drifts mobile oxygen vacancies (or metal ions from an active electrode) to grow a conductive filament across the gap; reversing the voltage retracts it. This 2D companion draws the same cross-section as a flat schematic instead of an orbiting 3D scene, so the filament's growth direction and jaggedness read directly off the diagram.
dw/dt = k·μ·I(t) filament state, clamped [0,1]
R(w) = R_on·w + R_off·(1-w)
I(t) = V(t) / R(w)
- Filament state w — fraction of the gap bridged by the conductive channel; w=1 is fully formed (low R_on), w=0 fully dissolved (high R_off).
- Ion mobility μ — how fast the filament responds to current; higher μ widens the hysteresis loop.
- R_off/R_on ratio — the device's ON/OFF contrast; larger ratios pinch the I-V loop into a sharper bowtie.
The signature is the pinched hysteresis loop: the I-V curve always passes through the origin (I=0 when V=0) but traces two different paths for rising and falling voltage — a shape no resistor, capacitor or inductor alone can produce. This nonvolatile, history-dependent resistance is the basis of RRAM memory and neuromorphic synapse chips.