Two-colour Patterns Gallery
Generated by the axes of the 16 families/generations, closed on the cube — select a pattern to see its tiling.
La Livrée d'Hermès is a book of philosophy and mathematics, freely available. This gallery is built from the verified catalogue of drawn axes, by XOR of chords, with geometric closure on the cube as the only selection criterion.
Loading the figures from data/bicolore_galerie_v1.json…
Frequently asked questions
What is a two-colour pattern in this gallery?+
Each pattern is the XOR of a non-empty subset (a chord) of the 16 base masks — the 4 two-colour families (Yin, Yin mutant, Yang, Yang mutant) at their 4 generations (T0 to T3), each generated by its own drawn axes.
Why 142 patterns and not 144?+
144 figures close on the cube at the cell grain (among the 8⁶ combinations of symmetries of the 6 faces, a dressing exists that makes the tint continuous from one face to the next). Two of them — plain light and plain dark — close trivially and are left out of the gallery: 142 patterns remain.
What does the grain change?+
The C8 grain reads the tint triangle by triangle (8 per cell, 1152 in all); the C1 grain reads it cell by cell (144 in all, a single bit per cell). The same chord of axes generates a different figure depending on the grain chosen — closure on the cube, for its part, is checked at the cell grain.
Where do the axes come from?+
From the verified catalogue of the work on the law of axes, parity and echoes: each family and each generation is a list of drawn lines (nature and offset), reproduced from the source plates.
Choose the grain and the colouring
Filter by status under the half-shift (6, 6)
Tiling of the selected pattern
Still wallpaper, in vector
A pattern from the corpus, read in two colours (the yellow cells become the triangles that complete the nearest colour), with a ground laid on each cell. A single SVG image with no resolution: it covers 1920 × 1080, 2560 × 1440, 4K and any other screen, for a few kilobytes. Its two colours are those of the gallery above.
The animation, in three colours or in this collection in two colours, is on the Wallpapers page.

