Gyre turn, wait, recolour
Three colours welded to a third-turn about a point of no symmetry. Turn the picture a third of a turn about p, run the film on a third of a period and step every colour back one, and nothing changes; do any two of the three and it does. A cyclic colour group is allowed to be fully entangled — nothing at all surviving in a single frozen frame — and that is the character this catalog was selected for; the counts below say how many of the admitted entries actually have it, and every entry says for itself, in its badges and in its own measured table. Every entry is a saved orbit of the named equation, carrying its own verification and a colour law re-derived from its own bytes at every node-frame.
1 · The base film group
The colour law is a theorem for any field on a triangular lattice and any turn centre, so every hexagonal film group can host it. What differs is what the picture then looks like, whether the argmax ever ties — where it does, the law fails at exactly those nodes and the field is refused — and whether any extra symmetry leaks into the colour-preserving subgroup.
The colour law is re-derived from the saved bytes at every node-frame before an entry is published, and the colour-preserving subgroup is measured by an exhaustive search over all twelve point operations, every node translation, every time shift and all six recolourings — not assumed.
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Parameters, thumbnails and the measured symmetry tables are precomputed.
Coin: the turn and how long you wait. Chip: what becomes of the colours.
Measured symmetry table
| Operation | Time | Colour | Agreement |
|---|
Numerical record
Only colourings whose law was re-derived from the saved bytes at every node-frame appear here.
Why some fields cannot host this colouring —
Every refusal is logged with its reason in colour-atlas-build.json, beside the catalog. A tie in the argmax is decided by index order, and the relabelling does not carry index order along, so the colour law fails at exactly the tied nodes: the builder measures the law rather than assuming it, and admits only an exact 1.
Entangled colourings · Trefoil · S₃ · Triskele (the split sibling) · The standalone Gyre page · Notation · How the patterns are computed