Spacetime Groups

Monochrome wallpaper group 3 of 17

∗∗ pm

Parallel mirrors. A colour-reversing mirror pins the contour: w vanishes identically along the line, so the mirror itself is drawn as a black/white boundary. The catalog holds 7 saved fields under a pm film group, read 31 different ways: 7 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 — 20 where s is free, and 4 plain thresholds to compare them with. Separately measured: 18 of the 31 exchange the two inks after half a period exactly.

1 · The film group

Each tile is a pm 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.

Fixed frame — the simulation’s own width
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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 — …

OperationWaitColoursResidual

Numerical record

Only pictures whose two-colour law was re-derived from the saved bytes at every node-frame appear here.