Module noise 

Noise functions for the Proof Engine mathematical renderer.

Implementations: Perlin 1-D / 2-D / 3-D, Simplex 2-D / 3-D, Cellular / Worley, Curl (divergence-free), Domain Warping, Ridged Multifractal, Billow, and Fractional Brownian Motion over each. All functions are stateless, deterministic, and seeded by a compile-time permutation table.

Functions

animated_noise

Animated noise — samples a moving “slice” through 3-D space. time advances the z coordinate, giving smooth noise animation.

billow

Billow noise — absolute-value fBm, gives cloud and pillow shapes. Output ≈ [-1, 1].

curl2

2-D curl noise. Returns a velocity vector tangent to the gradient of the underlying Perlin field — zero divergence means no sources/sinks.

curl3

3-D curl noise — divergence-free velocity field in 3-D. Uses three separate Perlin potentials for the three curl components.

curl2_fbm

2-D curl noise with fBm underneath — richer turbulent flows.

domain_warp

Domain-warped fBm — feeds noise output back into coordinates. Produces the swirling, self-similar patterns seen in marble, flame, and procedural nebulae. warp_strength controls how much to offset coordinates.

domain_warp2

Two-level domain warp — deeper self-similarity, heavier compute cost.

domain_warp3

3-D domain warp.

fbm

Classic 2-D fBm over Perlin noise.

fbm1

1-D fBm over Perlin noise — useful for audio modulation and time curves.

fbm3

3-D fBm over Perlin noise.

fbm_simplex

2-D fBm over Simplex noise — tighter, more crystalline features.

from_01

Remap from [0, 1] to [-1, 1].

gradient_2d

Generate a gradient field direction from noise — useful for steering particles.

gradient_3d

Generate a 3-D gradient vector from noise.

noise1

1-D value noise (smooth random walk), good for audio modulation.

perlin1

1-D Perlin noise. Output ≈ [-1, 1].

perlin2

2-D Perlin noise. Output ≈ [-1, 1].

perlin3

3-D Perlin noise. Output ≈ [-1, 1].

quick_noise

Smooth noise at a position with no configuration — sensible defaults. Output in [0, 1].

ridged

Ridged multifractal — sharp ridges, excellent for lightning, cracks, and mountain terrain. Output ≈ [0, 1].

ridged3

Ridged 3-D variant — useful for volumetric density fields.

sample3

Sample 3-D Perlin noise at a world position.

sample_curl3

Sample curl noise at a 3-D world position.

sample_fbm3

Sample 3-D fBm at a world position.

simplex2

2-D Simplex noise. Output ≈ [-1, 1]. Sharper features than Perlin.

simplex3

3-D Simplex noise. Output ≈ [-1, 1].

tiled_perlin2

Tiled 2-D Perlin noise — wraps seamlessly at (tile_w, tile_h). Useful for seamless texture generation.

to_01

Remap from Perlin’s [-1, 1] to [0, 1].

turbulence

2-D turbulence — classic signed-to-abs fBm, used for marble veining.

turbulence1

1-D turbulence (abs fBm) — good for entropy ripple and heat haze.

worley2

Cellular / Worley noise. Returns (f1, f2) — distances to nearest and second-nearest cell point.

worley3

3-D Worley noise.

worley_crackle

f2 - f1 — highlights cell borders, useful for vein / crack patterns.

worley_f1

Nearest-cell Worley, clamped to [0, 1].

worley_fbm

Worley fBm — octave-stacked cellular noise for complex surface patterns.