FROM AN ADDRESS TO A WORLD
A courtyard written in ranges, stripes, sieves, and stacks.
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Tap a triangle, column, wall, or slab to read the rule behind it.
Integer coordinates give every cell a stable address. Square-shell indexing addresses the cells; the power-of-two ruler rank v₂(n) shapes repeating structure. Two triangle addresses belong to each cell.
q = max(x,z); t = 2·squareIndex(x,z) + sideEvery courtyard façade reserves a two-unit opening at coordinate 12. Room dividers share two-unit openings too. These portal rules feed both geometry and collision, so openings remain passable as the sieve changes.
portal = { center: 12, width: 2, headroom: 2.4 }The range and stride select columns. The XOR sieve opens windows. The central 8 × 8 region stays unbuilt at each stacked level. Paths cross the courtyard, with continuous floor triangles beneath them.
select(n) = start ≤ n ≤ end ∧ (n − start) mod stride = 0THE MATH UNDER THE PLAYGROUND
Your four original interactive experiments are preserved: square-XOR indexing, the pure-add mask, Pascal’s bit-addressed triangle, and subset walking versus direct access.
Open the interactive math lab ↗Terrain now samples the actual Ruler Foundry field at shared vertices: square shells, v₂ ruler ranks, terraces, and XOR/residue sieves. Triangle grouping and architecture are prototype extensions. Shared-vertex continuity is the edge rule implemented here; the walking scene adds an entry path, two connected rooms, and collision from the wall records.
ENTRY PATH
Tap courtyard geometry to inspect its address and rule.