A row of pendulums whose lengths are tuned so that neighbours differ by exactly one swing per cycle: the front view, the live wave pattern and the length table.
The science
Pendulum i (counting from 0) is tuned to complete n_i = N0 + i swings in the cycle time T, so its period is T_i = T / n_i. For a small swing the period of a simple pendulum is T_i = 2 pi sqrt(L_i / g), hence the length L_i = g (T / (2 pi n_i))^2. Longer pendulums have fewer swings. The displacement of pendulum i is theta_i(t) = A cos(2 pi n_i t / T), the same kinematics as the 3D page.
Because neighbours differ by exactly one swing per cycle, the phase difference between neighbours grows by 2 pi t / T. At t = 0 and t = T every phase is equal and the row lines up. At t = T/2 neighbours are in antiphase. In between the bobs trace travelling waves, standing waves and apparent chaos, a beat pattern like two close tones.
Simplifications: a true pendulum with a large amplitude is slower by the factor 1 + A^2/16 + ... (shown in the readouts), so a real set would need to be tuned for the amplitude; no damping and no air drag. Checks below: a time-stepped RK4 pendulum of the longest length against its design period, and the exact realignment of all phases at the end of the cycle.