feat(stdlib): add Noise.* — deterministic fixed-point procedural noise (#3)
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A Noise.* namespace for procedural generation, implemented entirely in Q16.16
fixed point over an integer permutation hash so a seed reproduces the exact same
field on every platform and run (native/headless/wasm) — the determinism edge
over float noise that drifts across CPUs.

  - value2 / perlin2 / simplex2  — value, gradient, and simplex noise -> [-1,1]
  - fbm2(x,y,seed,octaves)       — fractal Brownian motion (octaves of simplex)
  - cellular2 / cellular2_id     — Worley F1 distance + nearest-cell id
  - unit(n)                      — remap [-1,1] -> [0,1]

Covers issue phases 1–2 fully plus cellular from phase 3; domain warp, ridged/
billow, and sample1/sample3 remain as follow-ups. Pure integer IR, C-free;
cellular/fbm reuse the math prelude's fx_sqrt.

- examples/library/noise.ludic: asserts the invariants a fixed-point generator
  must hold (Perlin == 0 at lattice points, every sampler within [-1,1],
  reproducibility, seed sensitivity, non-negative cellular distance). Wired into
  `x test` (now 52 passed).
- docs: a new Noise section + per-symbol pages; inventory and coverage pass.
- seed regenerated; `x bootstrap-cfree` fixpoint holds.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
This commit is contained in:
Orkun ÇAKILKAYA 2026-08-30 21:50:50 +03:00
parent 2ddf830f0b
commit a4f1494a04
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---
id: noise-cellular2_id
name: Noise.cellular2_id
category: noise
kind: namespace-method
tokens: Noise.cellular2_id
sig: Noise.cellular2_id(x, y, seed) -> int
tip: The id of the nearest Worley cell — stable per cell.
order: 6
ns: Noise
member: cellular2_id
---
Returns the integer **id of the nearest cell** in the same Worley diagram that <a href="noise-cellular2"><code>Noise.cellular2</code></a> measures distance in — a stable hash that is identical for every sample point inside a given cell. Use it to assign something discrete per region: the biome or material of a cell, the variant of a scattered prop, a per-region colour. Combine it with the F1 distance to shade toward cell edges.
The id is a hash, so treat it as an opaque label (mod it into your table of choices); it is deterministic across platforms and runs.
Parameters:
- `x`, `y` — the sample coordinates (`fixed`)
- `seed` — the field selector (must match the `cellular2` call it pairs with)
```ludic
program CellId {
entry {
let seed = 7
let id = Noise.cellular2_id(fixed(5) / fixed(4), fixed(3) / fixed(4), seed)
let biome = Math.posmod(id, 4) # one of 4 biomes for this cell
print(biome)
}
}
```