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Every beginning of the planar three-body problem, in a navigable atlas. Simulated and drawn on the GPU or CPU. Explore and measure the symmetry-reduced space of initial conditions through arbitrary 2-plane charts.

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Principia. Planar Three-Body Problem. A slice of the planar three-body problem, drawn in pencil: dark rippled bands on the left break into pale curling filaments that sweep across the page.

You are looking through a slice of every possible beginning of the three-body problem. Each point is a complete starting configuration (three masses, their positions and velocities), followed forward until its fate is known. The colour records that fate.

The slice is a flat plane through an eight-dimensional space of starting conditions. It can be moved, rotated and tilted to look along any direction. Where two fates meet, the boundary is not a line: zoom in and it opens into finer structure without end.

Principia is the instrument that makes these pictures, and measures what they show. Where it can't trust a result, it says so, rather than colouring a guess.

A slice in watercolour and pencil: nested arches of every colour, folding ever finer towards their centre. A slice drawn in pencil: three-fold petals of graphite meeting at a point. A slice in watercolour and pencil: red and cyan washes wound into a tight spiral. A slice in watercolour and pencil: brick red, blue and green washes twisting into a pale centre.

A slice in watercolour and pencil: a fan of fine arches in red, cyan and green, rising from one edge. A slice drawn in pencil: curling eddies in graphite above a pale, smudged shelf. A slice in watercolour and pencil: red, green and blue bands wound around a small bright vortex on black.

AtlasBrowse the space of beginnings on the GPU, natively, or in the browser as the same app. Pan, zoom without end, and rotate or tilt the slice in any direction.
ChartsFlat slices, the shape sphere, Burrau's problem, or a chart built from any axes you choose.
FateEvery point integrated forward, regularised through close encounters, until a body escapes, two collide, or time runs out.
RefinementSamples go where fates change, and stay coarse where they don't.
StainA graph from what was measured to how it looks, printed in watercolour, pencil or ink. The data doesn't change, only the ink.
InspectorFollow one beginning closely, at double precision, and watch its orbit.
HonestyIt shows where its precision runs out: open any point to watch its single- and double-precision orbits part, and when. Failed runs are kept and counted, never painted over.
PrintsEvery image carries its own settings, so any view can be recreated from the picture alone.
ResultsBrowsing buys hypotheses; the batch job, run at full precision, buys results.

Under construction. The foundations are laid, and the interface already runs against a stand-in engine.

Build progress: one square per task of the plan, by milestone from M0 to M8, inked when merged, washed in ochre when in review and outlined when not started, with each milestone's share done and the overall percentage.

A slice in watercolour: escape and collision basins in rose, ochre, cerulean and sienna, folding into one another across a field of Payne's grey.

-M '26

About

Every beginning of the planar three-body problem, in a navigable atlas. Simulated and drawn on the GPU or CPU. Explore and measure the symmetry-reduced space of initial conditions through arbitrary 2-plane charts.

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