Free Electron Gas 2D: Drude Drift-Velocity Convergence

This is the 2D counterpart to the 3D Drude free-electron model, built as an independent simulation rather than a re-rendered scene. A genuine 2D gas of conduction electrons scatters off the lattice as a Poisson process with rate 1/τ while also colliding elastically with itself — a real hard-disk gas mechanic the 3D version does not include — and accelerates under the applied field between scatters. Because elastic collisions conserve total momentum, turning those electron-electron collisions on or off leaves the drift readouts unchanged, a directly checkable consequence of the physics. A live running-average chart tracks the simulated ensemble's mean forward velocity against the closed-form analytic prediction v_d = eEτ/m, converging visibly as more samples accumulate after every field, temperature or material change.