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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>
31 lines
1.3 KiB
Markdown
31 lines
1.3 KiB
Markdown
---
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id: noise-fbm2
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name: Noise.fbm2
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category: noise
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kind: namespace-method
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tokens: Noise.fbm2
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sig: Noise.fbm2(x, y, seed, octaves) -> fixed
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tip: Fractal Brownian motion — octaves of simplex, in [-1, 1].
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order: 4
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ns: Noise
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member: fbm2
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---
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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.
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Each octave uses a different derived seed, and the whole thing is deterministic in fixed point across platforms and runs.
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Parameters:
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- `x`, `y` — the sample coordinates (`fixed`)
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- `seed` — the base field selector (each octave derives from it)
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- `octaves` — how many layers to sum (higher = more detail)
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```ludic
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program Fbm {
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entry {
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let seed = 1337
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let h = Noise.fbm2(fixed(2) / fixed(7), fixed(9) / fixed(7), seed, 5)
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print(Math.floor(Noise.unit(h) * fixed(100))) # detailed 0..100 height
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}
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}
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```
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