2D Pendulum Wave — Numerically Integrated Pendulum Row

This 2D side-view companion to the 3D Pendulum Wave laboratory runs a row of genuinely independent simple pendulums, each with a real, precisely different length set by the classic pendulum-wave design rule L_n = g·T_n²/(4π²). Every frame, each pendulum's angle is advanced by RK4-integrating its own real equation of motion theta'' = -(g/L)·sin(theta) — the travelling-wave, standing-wave and chaotic-looking patterns you see, and the exact moment they snap back into a single line, are all emergent consequences of that per-pendulum dynamics rather than a pre-scripted phase animation.