The hunt for new orbits.
Your browser traces fresh starting conditions with the exact equations of motion and tries to close the paths that nearly return. Those that do are checked at high precision before they count.
Each test is one starting arrangement of three masses, traced for a few dozen time units with unsoftened Newtonian gravity. The kernel records how far the path is from its start at every step and, from the closest returns, runs a bounded Newton shooting on the initial conditions and the period.
“Didn’t close” means no closing orbit was found within this test’s limits, not that none exists. A “promising return” is a proposal: the campaign server first checks whether it is a loop this search already verified or an orbit of the atlas, and records it as that orbit if so. What remains is refined to 106 bits by the finder’s own browser and confirmed by the server in double precision; a loop that would carry a stable label, a new topology or a name, and one in twenty of the rest, is recomputed by the server at 160 and 192 bits. Only a verified periodic result reaches the checked loops, labelled linearly stable or unstable for small planar perturbations, and each says which of the two confirmed it. Known reference orbits are placed in the stream on purpose, to check the numerics, and are labelled as such.
Every checked loop is compared with the atlas by its scale-free period and the shape of its three pairwise distances; a match is labelled as that known orbit and links to it, and a loop traversed several times is reduced to its primitive period. Its braid, the sequence of moments at which the bodies line up, is compared with the atlas too: a sequence the atlas does not have is a new topology. Whether an unmatched loop is new remains for review. Nothing here is added to the atlas automatically.
A fifth of the tests are fresh random seeds, the unbiased baseline. The rest go to the kinds of seed whose checked loops have turned out new most often, or start beside loops this search has already checked, since the neighbourhood of a find is where its relatives are. A family the search already holds twenty loops of at a mass class is not recorded further, and the search is steered away from it; the kernel reads a promising return’s braid word itself, so such a member is declined in the browser and only a note of it is uploaded; the server re-reads the notes when it has time.