∗333 p3m1
Third turns with mirrors through every centre. On the triangular lattice the mirror is the operation that exchanges the inks, and its axis is drawn on the picture. The catalog holds 19 saved fields under a p3m1 film group, read 87 different ways: 15 where the operation s is itself a spacetime symmetry of the wave — so s and the half-period wait are two names for one antisymmetry — 59 where s is free, and 13 plain thresholds to compare them with. Separately measured: 49 of the 87 exchange the two inks after half a period exactly.
1 · The film group
Each tile is a p3m1 film group — the same wallpaper group with a different assignment of time shifts to its operations — and counts the distinct pictures the catalog holds under it. A field filed under more than one film group appears under each.
2 · The rule that makes two colours
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Plume Monochrome — “the wave”the first of these pictures, on its own endless page · 16 + 16
Weave Monochrome — “the weave”the same rule on a woven sibling · 32 + 32
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Parameters, thumbnails and the measured two-colour tables are precomputed.
The marks are off on every animation on this site. Tick the box, or press G, to draw the operations of the two-colour group over the picture.
The measured two-colour group — …
| Operation | Wait | Colours | Residual |
|---|
Numerical record
Only pictures whose two-colour law was re-derived from the saved bytes at every node-frame appear here.
All 17 wallpaper groups · The same fields in ember (p3m1) · Weave Monochrome · Plume Monochrome · Entangled colourings · How the patterns are computed