◦ p1
Translations only. Each entry below is one way the group's operations can advance a periodic pattern in time, from the clockwork/colouring correspondence; every animation is a saved, independently re-verified solution of the named equation.
1 · The time symmetry
This wallpaper group has one catalog entry, the zero-offset reference: every operation acts at the same instant, so its patterns are ordinary periodic animations with the full spatial symmetry.
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Parameters, thumbnails and numerical checks are precomputed.
Symbols: time-shift symmetry. Curved arrows: measured local motion.
Numerical record
The displayed width is measured in simulation lattice lengths L.
Only accepted numerical orbits appear here. An empty entry means existence remains unresolved.
All 17 wallpaper groups · Research note · How the patterns are computed