The pendulum synchronization effect is the opposite of your claim. It has a physical causal reason for why pendulums become synchronized. Your claim is that it was random and independent.
replyI think you are talking about two different things.
replyPhysically coupled pendulums will sync up (adjust their period to match).
But, physically uncoupled (fully independent) pendulums with differing periods will occasionally appear to take a swing or two in sync.