Exact integer arithmetic on the Eisenstein A₂ hexagonal lattice for build placement and pathfinding
Project description
Slackwater Lattice
Build placement on the Eisenstein A₂ hexagonal lattice. Isotropic. Exact. Beautiful.
A Python + Lua package that snaps all build placements to a hexagonal lattice. Guarantees minimum spacing, eliminates floating-point drift, and produces visually organic tidal-community architecture.
What it does
- EisensteinInteger: exact arithmetic on the hexagonal lattice (no floats)
- LatticeSnap: snap any (x, z) position to the nearest lattice point
- LatticeNeighbors: find the 6 equidistant neighbors of any point
- LatticePath: plan a path through the lattice (for bridges, roads, conveyor belts)
- LatticeDensity: measure how dense a build is (harmony governor input)
Why hexagonal?
Square grids have a 41% diagonal penalty — neighbors aren't equidistant. Hexagonal lattices have 6 equidistant neighbors at exactly distance 1. Agreement is isotropic. Error is uniform. The math is exact integer arithmetic, inspired by the FLUX constraint engine.
Related
- Snapkit v2 — the triadic cognitive architecture this lattice supports
- Constraint Theory Math — the mathematical foundations
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