Indexing the archive…
Your Universe of Digital Possibilities
Three suns, one law — Newton’s gravity, exact and reversible. For two bodies it closes into an eternal ellipse; for three there is no formula at all (Poincaré, 1890), and the motion is chaotic. On load they run the figure-eight choreography, the rare dance that holds. Turn the Perturbation knob and watch it smear into chaos; load the Pythagorean preset to see the usual fate — a binary, and a sun flung out forever. Drag a sun to set it loose yourself.
Every mass pulls every other. ε is Plummer softening — it rounds off the 1/r² singularity so a near-collision integrates cleanly instead of exploding.
Integrated by velocity-Verlet (leapfrog) — symplectic, so energy stays bounded over thousands of periods. The drift readout proves the orbits are the law’s, not the solver’s.
Poincaré proved (1890) there are no further analytic integrals: the three-body problem is non-integrable. This is the historical birthplace of chaos theory.
A measure-zero set of exact periodic orbits survives the chaos — Euler’s collinear line, Lagrange’s equilateral triangle (the origin of the L-points), and the figure-eight.
The two-body problem is the universe physics dreamed of — exact, eternal, solvable. The three-body problem is the one we live in, and the first proof that a law can be perfectly known and the future still beyond reach. The Divergence (INST·05) measures this same exponential separation on a pendulum and named the Solar System as a chaos horizon — Laskar showed the inner planets are chaotic with a Lyapunov time of about five million years. This is that horizon, drawn in the sky. And where The Well (INST·07) shows gravity as the geometry that bends light, this shows its other face — the dynamics that moves the worlds. The figure-eight is the quiet counter-melody: order is not impossible in chaos, only rare, exact, and easily lost.