Spacetime Groups

Time-shift symmetries

Periodic reaction–diffusion patterns

Saved periodic solutions of three equations — Gray–Scott, complex Ginzburg–Landau and the Brusselator — whose wallpaper-group operations advance the pattern by prescribed fractions of its period, grouped by wallpaper group. Each entry is one row of the clockwork/colouring correspondence; every animation was re-verified from its saved bytes.

The 17 wallpaper groups

Only numerically verified periodic patterns appear in the galleries. Counts are loaded from the saved index; each card also opens without them.