Noise represents a function from a Seed and coordinates p to a noise value v.

For convenience, dimension-specific type aliases are provided:

Use warp to transform coordinates and remap (or fmap) to transform values.

To evaluate noise functions, use noise1At, noise2At, or noise3At

NB: Noise is a lawful Profunctor where lmap = warp and rmap = remap. There are some useful implications to this, but pure-noise is committed to a minimal dependency footprint and so will not provide this instance itself.

Algebraic composition

combined :: Noise (Float, Float) Float
combined = (perlin2 + superSimplex2) / 2

Coordinate Transformation

scaled :: Noise2 Float
scaled = warp (\(x, y) -> (x * 2, y * 2)) perlin2

Seed value for deterministic noise generation.

Using the same Seed value will produce the same noise pattern, allowing for reproducible results. Different seed values produce different, independent noise patterns.

Evaluate a 1D noise function at the given coordinates with the given seed. Currently, you must use a slicing function like sliceX to reduce higher-dimensional noise into 1D noise.

Evaluate a 2D noise function at the given coordinates with the given seed.

Evaluate a 3D noise function at the given coordinates with the given seed.

2D Perlin noise. Classic gradient noise algorithm.

3D Perlin noise. Classic gradient noise algorithm.

2D OpenSimplex noise. Smooth gradient noise similar to Perlin but without directional artifacts.

2D SuperSimplex noise. Improved OpenSimplex variant with better visual characteristics.

2D Cellular (Worley) noise. Configure with CellularConfig to control distance functions and return values.

Cellular noise creates patterns based on distances to randomly distributed cell points.

Configuration for cellular (Worley) noise generation.

Cellular noise is based on distances to randomly distributed cell points, creating a distinctive cellular or organic pattern.

Default configuration for cellular noise generation.

Distance function for cellular noise calculations.

Different distance metrics produce different visual characteristics in the cellular pattern.

What value to return from cellular noise evaluation.

These options allow for different visual effects by returning different properties of the cell structure.

2D Value noise. Simple noise based on interpolated random values at grid points.

2D Value noise with cubic interpolation for smoother results.

3D Value noise. Simple noise based on interpolated random values at grid points.

3D Value noise with cubic interpolation for smoother results.

A noise function that produces the same value everywhere. Alias of pure.

A noise function that produces the same value everywhere. Alias of pure

Used to provide the Num instance.

Transform the values produced by a noise function.

This is an alias for fmap. Use it to transform noise values after generation:

Examples

-- Scale noise from [-1, 1] to [0, 1]
normalized :: Noise2 Float
normalized = remap (\x -> (x + 1) / 2) perlin2

Transform the coordinate space of a noise function.

This allows you to scale, rotate, or otherwise modify coordinates before they're passed to the noise function:

NB: This is contramap

Examples

-- Scale the noise frequency
scaled :: Noise2 Float
scaled = warp (\(x, y) -> (x * 2, y * 2)) perlin2

-- Rotate the noise field
rotated :: Noise2 Float
rotated = warp (\(x, y) -> (x * cos a - y * sin a, x * sin a + y * cos a)) perlin2
  where a = pi / 4

Modify the seed used by a noise function.

This is useful for generating independent layers of noise:

See also next2 and next3 for convenient increment-by-one variants.

Examples

layer1 = perlin2
layer2 = reseed (+1) perlin2
layer3 = reseed (+2) perlin2

combined = (layer1 + layer2 + layer3) / 3

Increment the seed for a 2D noise function. See reseed

Increment the seed for a 3D noise function. See reseed

Slice a 2D noise function at a fixed X coordinate to produce 1D noise.

Examples

noise1d :: Noise1 Float
noise1d = sliceX2 0.0 perlin2  -- Fix X at 0, vary Y

-- Evaluate at Y = 5.0
value = noise1At noise1d seed 5.0

Slice a 3D noise function at a fixed X coordinate to produce 2D noise.

Examples

noise2d :: Noise2 Float
noise2d = sliceX3 0.0 perlin3  -- Fix X at 0, vary Y and Z

-- Evaluate at Y = 1.0, Z = 2.0
value = noise2At noise2d seed 1.0 2.0

Slice a 2D noise function at a fixed Y coordinate to produce 1D noise.

Examples

noise1d :: Noise1 Float
noise1d = sliceY2 0.0 perlin2  -- Fix Y at 0, vary X

-- Evaluate at X = 5.0
value = noise1At noise1d seed 5.0

Slice a 3D noise function at a fixed Y coordinate to produce 2D noise.

Examples

noise2d :: Noise2 Float
noise2d = sliceY3 0.0 perlin3  -- Fix Y at 0, vary X and Z

Slice a 3D noise function at a fixed Z coordinate to produce 2D noise.

This is useful for extracting 2D slices from 3D noise at different heights:

Examples

heightmap :: Noise2 Float
heightmap = sliceZ3 10.0 perlin3  -- Sample at Z = 10

Apply Fractal Brownian Motion (FBM) to a 2D noise function.

FBM combines multiple octaves of noise at increasing frequencies and decreasing amplitudes to create natural-looking, multi-scale patterns. This is the standard fractal noise implementation.

fbm :: Noise2 Float
fbm = fractal2 defaultFractalConfig perlin2

Apply Fractal Brownian Motion (FBM) to a 3D noise function.

3D version of fractal2. See fractal2 for details.

Apply billow fractal to a 2D noise function.

Billow creates a cloud-like or billowy appearance by taking the absolute value of each octave. This produces sharp ridges in the negative regions of the noise, creating a distinct puffy or cloudy look.

clouds :: Noise2 Float
clouds = billow2 defaultFractalConfig perlin2

Apply billow fractal to a 3D noise function.

3D version of billow2. See billow2 for details.

Apply ridged fractal to a 2D noise function.

Ridged creates sharp ridges by inverting and taking the absolute value of each octave. This is particularly useful for terrain generation, creating mountain ridges and valleys.

mountains :: Noise2 Float
mountains = ridged2 defaultFractalConfig perlin2

Apply ridged fractal to a 3D noise function.

3D version of ridged2. See ridged2 for details.

Apply ping-pong fractal to a 2D noise function.

Ping-pong creates a wave-like pattern by folding the noise values back and forth within a range, creating a distinctive undulating appearance. The strength parameter controls the intensity of the ping-pong effect.

waves :: Noise2 Float
waves = pingPong2 defaultFractalConfig defaultPingPongStrength perlin2

Apply ping-pong fractal to a 3D noise function.

3D version of pingPong2. See pingPong2 for details.

Configuration for fractal noise generation.

Fractal noise combines multiple octaves (layers) of noise at different frequencies and amplitudes to create more complex, natural-looking patterns.

Default configuration for fractal noise generation.

Strength parameter for ping-pong fractal noise.

Controls the intensity of the ping-pong folding effect. Higher values create more frequent oscillations.

Default ping-pong strength value.

Clamp a value to a specified range.

Returns the value if it's within bounds, otherwise returns the nearest boundary.

Clamp the output of a 2D noise function to the range [lower, upper].

Clamp the output of a 3D noise function to the range [lower, upper].

cubic interpolation

hermite interpolation

Linear interpolation between two values.

Monotonic lerp

quintic interpolation