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Two tilings join the catalogue, the 37th and 38th patterns, both from a study of the Bauhaus line-and-circle posters.
Bauhaus Tiles is one engine for the whole genre. Every glyph is a bundle of N parallel stripes following a line, a quarter arc, its straight chord, or an L-shaped elbow inside a square cell, placed so that stripe k crosses every cell side at the same fraction (k + ½)/N. That single constraint is what makes pipes, half discs, chevrons, nested diamonds, hatch blocks and woven knots all join across any edge in any rotation or reflection; Truchet's arc tiles are the N = 1 case. Nine motifs, four plane groups over a seeded block (free, pmm, p4m, p4), strokes or solid bands.
The drawing does not go cell by cell. It traces every band chain — side to neighbouring side across the grid, border to border or around a loop — and places each stripe by where it crosses the chain's entry edge, propagated step by step through the corner connectors. That is what lets the entire field slide with phase without a seam: mirrored, the sliding stripes become rings radiating from every disc centre. Closed loops whose round trip returns a stripe on the other side of its band are Möbius; no consistent shift exists on them, so they are detected and held still. A full cycle reproduces the first frame byte for byte.
Ring Scales is the seigaiha lattice: discs of one radius on a staggered grid, drawn in painter's order so each covers the one above it, with bold rings and a fine polar grid alternating by seed. Ring radii advance with phase.
Also in this release
- Both patterns ship with animation presets: Roll (bass on stripe weight, brightness on a weight gradient across the band) and Sections (a 16-beat step through the four symmetry groups, so a section change reads as order arriving) for the tiles; Ripple for the scales.
- The research note behind the two patterns is in
docs/research/: which Bauhaus families reduce to formulas, and which do not.
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