whatThree equal masses, pure gravity, a symplectic leapfrog that subdivides its step through close encounters and posts its energy error in the corner. Three ways to begin: a seeded random draw, Lagrange's rotating triangle of 1772, and the Chenciner-Montgomery figure-eight of 2000 -- three bodies sharing one track, each a third of a period behind the next.

whyThe claim is the famous one: the generic three-body system is not an orbit but a drawn-out negotiation that ends the same way almost every time -- two bodies bind, the third is thrown clear. The lottery tallies every draw's survival time. The triangle, beautiful and secretly unstable for equal masses, holds a few turns while instability grows out of rounding error, then shatters the same way. The eight simply refuses to die -- until you click: a one-percent nudge, and lap by lap the choreography unravels into the same old ending.

howKick-drift-kick at dt 5e-4 with 2x to 32x substepping keyed to the closest pair; ejection is called only when a body is far out AND unbound from the remaining pair. The energy ledger restarts at your nudge so the drift it reports is the integrator's own. One integer seeds every draw and every nudge; ink accumulates where the bodies have been.