Noise Taxonomy

Comprehensive guide to noise types in unshape: what they are, when to use them, and why we have so many.

Why So Many Noise Types?

Different noise types serve different purposes:

1. Spectral properties - How energy is distributed across frequencies (white, pink, brown, blue, violet)
2. Spatial correlation - How neighboring samples relate (uncorrelated vs coherent)
3. Visual/audio character - Smooth gradients vs sharp cells vs random static
4. Performance tradeoffs - Simple hashing vs expensive generation

No single noise type serves all needs, so we provide a comprehensive toolkit.

The Matrix

Type	1D	2D	3D	Character	Use Cases
White	WhiteNoise1D	WhiteNoise2D	WhiteNoise3D	Uncorrelated static	Dithering, randomization, audio hiss
Perlin	Perlin1D	Perlin2D	Perlin3D	Smooth gradients	Terrain, clouds, organic patterns
Simplex	Simplex1D	Simplex2D	Simplex3D	Smooth, less artifacts	Same as Perlin, better quality
Value	Value1D	Value2D	Value3D	Grid-aligned smooth	Fast approximation of Perlin
Worley	Worley1D	Worley2D	Worley3D	Cellular/distance	Event timing, cells, caustics
Blue	BlueNoise1D	BlueNoise2D	BlueNoise3D*	Well-distributed	Optimal dithering, sampling
Pink	PinkNoise1D	PinkNoise2D	-	Natural 1/f	Audio, natural phenomena
Brown	BrownNoise1D	BrownNoise2D	-	Random walk	Deep rumble, terrain, drift
Violet	VioletNoise1D	-	-	High-frequency	Audio dithering
Grey	GreyNoise1D	-	-	Perceptually flat	Tinnitus masking, audio testing
Velvet	VelvetNoise1D	-	-	Sparse impulses	Efficient reverb, decorrelation

*Blue noise 3D is expensive (O(n³), clamped to max 32³) - use with caution or pre-generate.

Spectral "Colors"

Noise color refers to spectral distribution, borrowed from light/audio terminology:

Power
  ^
  |██                          Brown (1/f²) - more bass
  |████                        Pink (1/f) - equal per octave
  |████████                    White (flat) - equal per Hz
  |      ████████              Blue (f) - more treble
  |          ████████          Violet (f²) - very high
  +-----------------------> Frequency

White Noise

• Spectrum: Flat - equal power at all frequencies
• Character: Pure static, uncorrelated samples
• 1D: Audio hiss, random jitter
• 2D: TV static, simple dithering (grainy)
• 3D: Volumetric randomness, temporal dithering

Blue Noise

• Spectrum: High-frequency bias
• Character: Well-distributed, no clumping
• Why optimal for dithering: Appears smoother to human vision
• Generation: Void-and-cluster algorithm (expensive)
• 2D: Primary use - image dithering
• 3D: Temporal stability in animations (very expensive to generate)

Pink Noise (1/f)

• Spectrum: Equal energy per octave
• Character: Natural, organic variation
• Why it sounds "natural": Many natural phenomena follow 1/f
• 1D: Audio (waterfalls, wind), heartbeat variation
• 2D: Natural textures, terrain details
• 3D: Not typically needed (use 2D + time)

Brown/Red Noise (1/f²)

• Spectrum: Strong low-frequency bias
• Character: Slow drift, random walk
• Named after: Brownian motion, not the color
• 1D: Deep rumble, slow parameter drift
• 2D: Smooth terrain base, fog density
• 3D: Not typically needed

Violet Noise (f²)

• Spectrum: Very high-frequency
• Character: Differentiated white noise
• 1D: Audio dither for high-freq content
• 2D/3D: Rarely useful (too high-frequency)

Grey Noise

• Spectrum: Psychoacoustically flat (weighted by human hearing)
• Character: Sounds equally loud at all frequencies (unlike white which sounds bright)
• Note: True grey noise requires ISO 226 equal-loudness weighting; we use an approximation
• 1D: Tinnitus masking, audio testing, perceptually neutral randomness
• 2D/3D: Not typically needed (it's about human hearing)

Velvet Noise

• Spectrum: Sparse impulses (not really a "color")
• Character: Mostly silence/neutral, occasional +1/-1 impulses
• Density: Controllable probability of impulse (typically 1-20%)
• 1D: Efficient convolution reverb, decorrelation, click textures
• 2D/3D: Not applicable (it's about sparse events in time)

Coherent vs Uncorrelated

Coherent Noise (Perlin, Simplex, Value)

• Nearby samples are correlated
• Produces smooth gradients
• Useful for: terrain, clouds, organic textures

Uncorrelated Noise (White, Blue)

• Each sample is independent
• No gradients, just points
• Useful for: dithering, random placement, audio

Why Certain Combinations Don't Exist

Missing	Reason
Pink/Brown 3D	Use 2D + time dimension instead
Violet 2D/3D	High-frequency in 2D/3D is just visual noise

Dimension Semantics

• 1D: Time (audio), scanlines, parameter curves
• 2D: Images, textures, terrain heightmaps
• 3D: Volumetric (fog, clouds), or 2D + time (animation)

3D for Temporal Stability

For animation, use 3D noise with z = time:

let noise = WhiteNoise3D::new();
// Same (x,y) at same time = same value
let v = noise.sample(Vec3::new(x, y, frame as f32 * 0.1), &ctx);

This gives temporally coherent randomness - no flickering between frames.

Performance Notes

Type	Speed	Notes
White	Fastest	Just hashing
Value	Fast	Interpolated hash
Perlin	Medium	Gradient interpolation
Simplex	Medium	Slightly better than Perlin
Worley	Slow	Distance calculations
Blue (generate)	Very slow	O(n²) or O(n³) generation

For real-time use:

• Prefer White/Value for simple randomness
• Use Perlin/Simplex for quality coherent noise
• Pre-generate blue noise textures
• Cache expensive noise in textures

FBM (Fractal Brownian Motion)

Layer multiple octaves of coherent noise for natural detail:

let terrain = Fbm2D::new(Perlin2D::new())
    .octaves(6)
    .lacunarity(2.0)
    .gain(0.5);

Available for all coherent noise types (Perlin, Simplex, Value).

Crate Organization

• unshape-noise: Raw noise functions (perlin2, worley3, etc.)
• unshape-field: Field wrappers (Perlin2D, Worley3D, etc.) implementing Field<I, O>
• unshape-image: Image-specific (BlueNoiseField, BayerField for dithering)

This separation allows:

• Using raw functions without the Field abstraction
• Composing noise fields with other fields
• Domain-specific optimizations (image dithering)