Nanorobot Swimmer 2D: Scallop Theorem & Phase Portrait

At the nanoscale, viscous drag overwhelms inertia — Purcell's scallop theorem says any actuator that simply retraces its own motion produces zero net swimming, no matter how fast it moves. This 2D simulator renders a three-link nanoswimmer (tail–mid–head) whose two hinges are driven with an adjustable phase offset, and integrates the geometric-phase "area rule" for low-Reynolds-number locomotion live, frame by frame. A dedicated phase-portrait panel traces the (φ₁, φ₂) loop whose enclosed area sets the thrust, and a scrolling velocity strip shows the instantaneous swim speed. Set the phase offset to 0° or 180° and watch the swimmer flap in place exactly as the scallop theorem predicts; move it toward 90° and a genuine non-reciprocal stroke opens up, producing real net displacement — with amplitude, frequency and fluid-viscosity controls to see how each shapes the swimming speed.