rind · ops — the tessellating weave, solved

the question

One hex packs 14 threads — 6 white + 8 production. Honeycomb it to make the world infinite. What happens to a thread where tile A's edge meets tile B's?

the solve

White = continuity. The hex has 6 edges; the cortex has 6 whites. Each white's rim-most cell claims one edge — an exact 1-white-per-edge bijection. Translation-tiling turns each owned white into a straight global strand, so the 6 whites collapse to 3 families: one azimuthal ring + two counter-rotating helices (the emergence, over the real Voronoi weave).

Production = K-doors. 8 engines don't divide the hex's 6-fold symmetry, so they can't all splice; they stay local and, where they graze the rim, abut the neighbour's other-kind thread — a cross-kind K-door. That is the K(6,8) contact reaching across the seam.

Continuity here is realised the way it is everywhere in rind: not literal curve-joining but door-adjacency between the rim cells that abut across the seam. Position along the edge decides which cell meets which.

beyond seven — the 3-coloured lattice

The hex centres form a triangular lattice, which is 3-colourable (colour = (i−j) mod 3). Each colour is a phase: an interleaved sub-lattice. Rotating one phase by a fixed 60° uses rotations, not reflections — and rotations compose consistently around a vertex (three chunks, all three colours, meet at every corner), so unlike the mirror it can't frustrate. phase cycles: off · CW60 dispersed (your proposal — the centre-colour rotated clockwise 60°) · pinwheel (the min-mismatch scheme found by search). rings grows the patch (7 → 19 → 37 chunks).

what the numbers say

Corners become nexus points — every vertex where three chunks meet (gold rings). Phase rotation lowers the overall seam mismatch by reorienting the production threads — but the white-only mismatch is rotation-invariant: the 6 whites exit 60° apart (a C6-symmetric set), so rotating a chunk maps that set onto itself and can't move where whites meet. Rotation relabels which family lands at a seam and reorients the spiral arms; it doesn't move the white exit points. (A mirror would — but you preferred no flip.) Watch the readout as you cycle phases.

the interface certificate

reading it

Grey hex = a chunk. Faint dots = the 14 threads. Bold lines = the 3 warp families along their true corridors; big dot = the hub, small dot = the rim exit. Dashed = the bridges joining families across seams. trace a family to isolate one. ◆/▬ (interfaces) = the K-doors / continuity. Drag to pan, scroll to zoom.