Each pendulum has a slightly different length, tuned so that pendulum k completes exactly n+k full oscillations in the cycle time T. The period of a simple pendulum is:
Solving for lengths: L_k = g (T / (n+k))²/ (4π²)
Because the frequencies are consecutive integers, the pendulums periodically realign after every full cycle, creating wave-like patterns, spirals, and apparent rotations — even though each individual pendulum is executing simple harmonic motion. This is a beautiful demonstration of superposition and interference.