∗2222 pmm
A rectangular grid of mirrors with half turns at the crossings. Which of them keep the colours and which exchange them is the whole content of the table below. The catalog holds 43 saved fields under a pmm film group, read 200 different ways: 42 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 — 133 where s is free, and 25 plain thresholds to compare them with. Separately measured: 112 of the 200 exchange the two inks after half a period exactly.
1 · The film group
Each tile is a pmm 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 (pmm) · Weave Monochrome · Plume Monochrome · Entangled colourings · How the patterns are computed