RULERS / LATTICES / ADDRESS STRIPES
Four patterns.
Four explanations.
Compare the same signed 16 × 16 window across column ranks, Gaussian ranks, address stripes and spatial corridors. Select a cell to expose the arithmetic.
Column rank is the exponent of base p in x − origin_x + 1. Gaussian rank counts exact divisions by 1 + i of (x − origin_x + 1) + (z − origin_z + 1)i.
Address stripes test (address − phase) mod period < width. Coordinate corridors test (x − origin_x − phase) mod period < width. These are different selections.
Base 2/3/5; threshold 0–16; period ≤1024. Window/origin coordinates and phase are bounded to ±1,000,000. The toolkit assigns zero rank at arithmetic zero; it is a convention, not a finite valuation of zero.