Each pendulum is a real physical pendulum with its own length Li, integrated with the true nonlinear equation of motion θ'' = −(g/L)sinθ − cθ' (RK4, not a linear approximation), so damping and the small nonlinearity at larger swings are both genuine. Lengths are picked so that, at the reference gravity, pendulum i completes exactly (30+i) full swings in one "resync cycle" — the classic pendulum-wave recipe. Because period T=2π√(L/g), raising or lowering g rescales every real period at once (and the whole cycle time with it) without touching a single length — a real physical consequence of the same masses on a different world, not a fake speed-up.
The phase-coherence readout R is a Kuramoto-style order parameter: R = |mean of eiθ over all pendulums| ⁄ amplitude-normalized, 1 when every pendulum is at the same phase of its swing and near 0 when phases are spread evenly — the same quantity used to quantify synchronization in coupled-oscillator physics.
T_i = 2π√(L_i/g) L_i chosen so T_i = T_cycle/(30+i)
θ_i'' = -(g/L_i) sinθ_i - c θ_i' (RK4 integration)
Click any bob to give it a "ghostly" push (an instant angular-velocity kick) — a real perturbation that knocks that one pendulum out of phase with the rest until damping and the natural period differences let it drift back into the pattern.