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-fbm2
name: Noise.fbm2
category: noise
kind: namespace-method
tokens: Noise.fbm2
sig: Noise.fbm2(x, y, seed, octaves) -> fixed
tip: Fractal Brownian motion — octaves of simplex, in [-1, 1].
order: 4
ns: Noise
member: fbm2
---
Samples **fractal Brownian motion** at <code>(x, y)</code>: it stacks <code>octaves</code> layers of <a href="noise-simplex2"><code>simplex2</code></a>, each at double the frequency and half the amplitude of the last, and normalises by the total amplitude so the result stays a <a href="type-fixed"><code>fixed</code></a> in <code>[-1, 1]</code>. Layering this way adds fine detail on top of broad shapes — the standard recipe for natural-looking terrain, clouds, and marble. More octaves means more detail (and more cost); 4–6 is typical.
Each octave uses a different derived seed, and the whole thing is deterministic in fixed point across platforms and runs.
Parameters:
- `x`, `y` — the sample coordinates (`fixed`)
- `seed` — the base field selector (each octave derives from it)
- `octaves` — how many layers to sum (higher = more detail)
```ludic
program Fbm {
entry {
let seed = 1337
let h = Noise.fbm2(fixed(2) / fixed(7), fixed(9) / fixed(7), seed, 5)
print(Math.floor(Noise.unit(h) * fixed(100))) # detailed 0..100 height
}
}
```