The neighbourhood
- Coordinates
- Square index n
- Cell inside patch
Gold notches are shared passage proposals. The first east/west crossing has two walkable wayhouses.
Address & recipe controls ↓ · Dataframe ↓
Read the arithmetic.
17 consecutive patches along X, beginning at your selection. Bars show v₂(X + 1); gold dots survive both the XOR sieve and density gate. Select a bar or row to travel there.
| Patch X / Z | Index n | √n floor | Remainder | v₂(n + 1) | mod 3 | mod 5 | Sieve residue | Density value | Keep | Kind |
|---|
n = root² + remainder · 0 ≤ remainder ≤ 2 × root · block size = 2 × root + 1. CSV also includes exact block size, low eight bits, ruler ranks and centre height. Import large coordinate/index columns as text to preserve them in spreadsheet software.
What does the mask reveal?
Start at the selected patch X. Square n, XOR the result, then measure the ordinary signed change. This arithmetic study does not change the terrain.
(s XOR m) − s = m − 2 × (s AND m), where s = n²
| n | n² | Low 5 bits | Shared bits / AND | n² XOR mask | Signed change | Direction | v₂(n) |
|---|
Every mask-5 case is determined by n mod 4. Mask 25 is determined by n mod 16. These are exact residue rules, not randomness claims. Zero uses the kit's ruler sentinel 0.