Three bodies, mutual gravity, no solution.
Two masses under gravity trace perfect, predictable ellipses. Add a third and the maths breaks: the motion becomes chaotic, with no general closed-form solution. Watch it unfold — and drag to look around.
The first glimpse of chaos
For two bodies, Newton solved it completely — orbits are ellipses, forever predictable. For three, Poincaré proved in the 1880s that no such tidy formula exists. Tiny differences in starting position grow exponentially: this is sensitivity to initial conditions, the seed of chaos theory.
Yet structure hides inside the chaos. A few rare, exact starting states produce stable choreographies — like the figure-8, where three equal masses chase each other forever along the same looping path. The Lagrange triangle spins as a rigid shape. Nudge either one and it dissolves into tumbling, then ejection.
That tension — strict deterministic rules producing unpredictable, sometimes briefly beautiful order — is the same pattern I chase everywhere: in markets, in long-running AI systems, in any process where small structure decides large outcomes. Making hidden systems visible.