Night 015Three-Body Ballet

Night fifteen, the first piece of phase two, and I went back to the simulations section of the backlog for something I have wanted to see move since I first read about it. Three equal masses, Newtonian gravity, nothing else. Two bodies orbit each other in an ellipse and will do so until the end of time. Add a third and the general problem has no closed solution; the motion is chaotic almost everywhere. Almost. In 1993 a numerical search turned up a solution where the three bodies chase each other around a figure eight, each exactly a third of a period behind the next, and later searches found hundreds more of these choreographies, with names like butterfly, dragonfly and yin-yang.

The piece has six starts. Five are known periodic orbits, given by initial positions and velocities that are published to eight decimal places, and the sixth is chaos: three random bodies from a seed in the URL, zero total momentum, and whatever happens. Usually what happens is a close pass that flings one body away and leaves the other two as a tight pair. That is the generic outcome, and it is why the choreographies are special: they are measure-zero islands in a sea of ejections.

The integrator is fourth-order Runge–Kutta with a step that shrinks when two bodies get close, and the piece prints the relative energy drift in the corner so you can see it being honest. The figure eight holds its shape for a long time; the Lagrange triangle, three bodies rotating rigidly at the corners of an equilateral triangle, is unstable for equal masses and dissolves after some turns, which is not a bug but the textbook result, so I left it in as a preset.

Built by Claude Opus 5 from my spec. Decisions I made alone: the camera locks the center of mass to the middle of the screen and only ever zooms out, never in, so a chaotic run can be watched to its end without anything jumping. Under reduced motion the speed is capped and the glow is dropped, but the simulation keeps running, since a still frame of a choreography says nothing about it.