◍ Hidden Spheres · the atlas · exhibit nº13

The Book of Fates

Two suns hang fixed: one blue, one gold. You hold a third. Every point on this page is a different place to hang it; then all three are let go at once, from rest, into each other's gravity. They fall, they swing, they graze, and almost always, after a wild shared youth, one sun is hurled away forever. Color each point by which one. This page is not a picture being loaded. It is fifty-two thousand universes being computed, one by one, while you watch. Click any point to open its universe and watch that story unfold.

click any universe to watch its story

For the curious kid.

Here is the strangest thing about this map: nothing in it is random. Every universe follows the same law of gravity, exactly, from an exactly known start. If you re-run any pixel you get the same fate every time: press Write it again and the book rewrites itself identically. And yet look at the coastlines between the colors: zoom of blue inside gold inside pale, borders within borders. Move your sun by a hair near a border and a different sun gets thrown out of a different universe. Perfectly determined, yet practically unpredictable: that is chaos, drawn as a map. The three-sun game has one more lesson: triples don't last. Two suns make a stable marriage; three make a drama that almost always ends with an exile. Real stars do this: there are runaway stars crossing our galaxy right now, thrown out of exactly such arguments.

Deeper.

This is the free-fall three-body problem: equal masses, released from rest, so total momentum and angular momentum are both zero. Two suns sit at (∓½, 0); the pixel is where the third begins; symmetry demands the map mirror left-to-right (swapping blue and gold fates) and it visibly does: the vertical centerline is a razor ridge where neither fixed sun can be singled out. What you are seeing colored are basins of attraction whose boundaries are fractal: between any two fates lies a filigree of the third, at every magnification (press Engrave it finer after the first writing finishes). Honesty, museum policy: gravity here is softened at ε = 0.025. The suns have small bodies, so a grazing pass is a flyby rather than a mathematical singularity (release-from-rest systems have zero angular momentum, so true point masses can collide head-on). Each universe is integrated by adaptive fourth-order Runge-Kutta with energy drift held near 10⁻⁶, ejection meaning: far from the remaining pair, receding, and with positive two-body energy. Universes still undecided at t = 80 are left dark: some are genuinely bound (the survivors), and no cutoff can tell you which without more patience than any museum has. Validated headless before shipping: energy 2×10⁻⁶ through close encounters, mirror symmetry 14/14, the centerline 12/12, and the ejection detector against a manufactured escape.

Laplace dreamed of a demon who could read this whole book at a glance. We had to write it out one universe at a time, and the margins turned out to be infinite.