Main view — a static orthographic 3-D shadow of principal axes 1, 2, 3 of the
pooled second moment (all N bodies, all samples). Depth is encoded as line opacity.
The stored coordinate basis is meaningless (the action is O(d)-invariant), and a plain
(1,2)-plane plot renders a large class of high-dimensional records as a featureless circle — hence 3-D.
Dots are the bodies, brightest first, body 0 ringed.
Strip — one panel per principal plane (1,2), (3,4), (5,6)…, in three states:
a curve = both axes live; a horizontal line = exactly one axis live;
a short grey rule = neither (or the axis does not exist). So
d = 2×(curve panels) + (line panels), countable by eye.
Panels are normalised per axis, so shape here is qualitative only.
Meter — under each panel, two bars of height √(λk/λ1):
the magnitudes the strip's per-axis normalisation throws away. Grey = dead axis;
a hairline = that axis does not exist at this d.
Ribbon — the mutual distances |q0−qk|(t), k = 1…⌊N/2⌋, over one
period, floor = 0. Dead-flat lines mean a relative equilibrium (rigid body rotation);
wavy lines mean a genuine choreography. The lowest minimum is minsep.
even speed — every orbit has the same period, so a loop whose path is 80 radii long
sweeps the frame ~15× faster than one 5 radii long. On, each tile's clock is divided by its own
path length so the grid reads at one pace; off, all tiles share the true time base.
dimension colour, fixed to 2…11 so it is stable across harvests:
Badges — rigid relative equilibrium
(rigidity < 1e-4, a clean gap in the data — trivial however high its d); frame {…} rotating
frame with its rotation-rate multiset; cover multiple
cover; family a continuous family (same N, same d, same action);
residual a record whose certified state exceeds 1e-9 or
whose stored coefficients exceed 1e-6.
Click any tile for the full record.