user: Describe Noise Utilities (mathutils.noise) from the Blender manual or Python API, including usage steps and snippets.

assistant: # Noise Utilities (mathutils.noise)

The Blender noise module.

mathutils.noise.cell(*position*, */*)
:   Returns cell noise value at the specified position.

    Parameters:
    :   **position** ([`mathutils.Vector`](mathutils.html#mathutils.Vector "mathutils.Vector")) – The position to evaluate the selected noise function.

    Returns:
    :   The cell noise value.

    Return type:
    :   float

mathutils.noise.cell_vector(*position*, */*)
:   Returns cell noise vector at the specified position.

    Parameters:
    :   **position** ([`mathutils.Vector`](mathutils.html#mathutils.Vector "mathutils.Vector")) – The position to evaluate the selected noise function.

    Returns:
    :   The cell noise vector.

    Return type:
    :   [`mathutils.Vector`](mathutils.html#mathutils.Vector "mathutils.Vector")

mathutils.noise.fractal(*position*, *H*, *lacunarity*, *octaves*, */*, *\**, *noise_basis='PERLIN_ORIGINAL'*)
:   Returns the fractal Brownian motion (fBm) noise value from the noise basis at the specified position.

    Parameters:
    :   - **position** ([`mathutils.Vector`](mathutils.html#mathutils.Vector "mathutils.Vector")) – The position to evaluate the selected noise function.
        - **H** (*float*) – The fractal increment factor.
        - **lacunarity** (*float*) – The gap between successive frequencies.
        - **octaves** (*int*) – The number of different noise frequencies used.
        - **noise_basis** (*Literal**[**'BLENDER'**,* *'PERLIN_ORIGINAL'**,* *'PERLIN_NEW'**,* *'VORONOI_F1'**,* *'VORONOI_F2'**,* *'VORONOI_F3'**,* *'VORONOI_F4'**,* *'VORONOI_F2F1'**,* *'VORONOI_CRACKLE'**,* *'CELLNOISE'**]**.*) – A noise basis string.

    Returns:
    :   The fractal Brownian motion noise value.

    Return type:
    :   float

mathutils.noise.hetero_terrain(*position*, *H*, *lacunarity*, *octaves*, *offset*, */*, *\**, *noise_basis='PERLIN_ORIGINAL'*)
:   Returns the heterogeneous terrain value from the noise basis at the specified position.

    Parameters:
    :   - **position** ([`mathutils.Vector`](mathutils.html#mathutils.Vector "mathutils.Vector")) – The position to evaluate the selected noise function.
        - **H** (*float*) – The fractal dimension of the roughest areas.
        - **lacunarity** (*float*) – The gap between successive frequencies.
        - **octaves** (*int*) – The number of different noise frequencies used.
        - **offset** (*float*) – The height of the terrain above ‘sea level’.
        - **noise_basis** (*Literal**[**'BLENDER'**,* *'PERLIN_ORIGINAL'**,* *'PERLIN_NEW'**,* *'VORONOI_F1'**,* *'VORONOI_F2'**,* *'VORONOI_F3'**,* *'VORONOI_F4'**,* *'VORONOI_F2F1'**,* *'VORONOI_CRACKLE'**,* *'CELLNOISE'**]**.*) – A noise basis string.

    Returns:
    :   The heterogeneous terrain value.

    Return type:
    :   float

mathutils.noise.hybrid_multi_fractal(*position*, *H*, *lacunarity*, *octaves*, *offset*, *gain*, */*, *\**, *noise_basis='PERLIN_ORIGINAL'*)
:   Returns hybrid multifractal value from the noise basis at the specified position.

    Parameters:
    :   - **position** ([`mathutils.Vector`](mathutils.html#mathutils.Vector "mathutils.Vector")) – The position to evaluate the selected noise function.
        - **H** (*float*) – The fractal dimension of the roughest areas.
        - **lacunarity** (*float*) – The gap between successive frequencies.
        - **octaves** (*int*) – The number of different noise frequencies used.
        - **offset** (*float*) – The height of the terrain above ‘sea level’.
        - **gain** (*float*) – Scaling applied to the values.
        - **noise_basis** (*Literal**[**'BLENDER'**,* *'PERLIN_ORIGINAL'**,* *'PERLIN_NEW'**,* *'VORONOI_F1'**,* *'VORONOI_F2'**,* *'VORONOI_F3'**,* *'VORONOI_F4'**,* *'VORONOI_F2F1'**,* *'VORONOI_CRACKLE'**,* *'CELLNOISE'**]**.*) – A noise basis string.

    Returns:
    :   The hybrid multifractal value.

    Return type:
    :   float

mathutils.noise.multi_fractal(*position*, *H*, *lacunarity*, *octaves*, */*, *\**, *noise_basis='PERLIN_ORIGINAL'*)
:   Returns multifractal noise value from the noise basis at the specified position.

    Parameters:
    :   - **position** ([`mathutils.Vector`](mathutils.html#mathutils.Vector "mathutils.Vector")) – The position to evaluate the selected noise function.
        - **H** (*float*) – The fractal increment factor.
        - **lacunarity** (*float*) – The gap between successive frequencies.
        - **octaves** (*int*) – The number of different noise frequencies used.
        - **noise_basis** (*Literal**[**'BLENDER'**,* *'PERLIN_ORIGINAL'**,* *'PERLIN_NEW'**,* *'VORONOI_F1'**,* *'VORONOI_F2'**,* *'VORONOI_F3'**,* *'VORONOI_F4'**,* *'VORONOI_F2F1'**,* *'VORONOI_CRACKLE'**,* *'CELLNOISE'**]**.*) – A noise basis string.

    Returns:
    :   The multifractal noise value.

    Return type:
    :   float

mathutils.noise.noise(*position*, */*, *\**, *noise_basis='PERLIN_ORIGINAL'*)
:   Returns noise value from the noise basis at the position specified.

    Parameters:
    :   - **position** ([`mathutils.Vector`](mathutils.html#mathutils.Vector "mathutils.Vector")) – The position to evaluate the selected noise function.
        - **noise_basis** (*Literal**[**'BLENDER'**,* *'PERLIN_ORIGINAL'**,* *'PERLIN_NEW'**,* *'VORONOI_F1'**,* *'VORONOI_F2'**,* *'VORONOI_F3'**,* *'VORONOI_F4'**,* *'VORONOI_F2F1'**,* *'VORONOI_CRACKLE'**,* *'CELLNOISE'**]**.*) – A noise basis string.

    Returns:
    :   The noise value.

    Return type:
    :   float

mathutils.noise.noise_vector(*position*, */*, *\**, *noise_basis='PERLIN_ORIGINAL'*)
:   Returns the noise vector from the noise basis at the specified position.

    Parameters:
    :   - **position** ([`mathutils.Vector`](mathutils.html#mathutils.Vector "mathutils.Vector")) – The position to evaluate the selected noise function.
        - **noise_basis** (*Literal**[**'BLENDER'**,* *'PERLIN_ORIGINAL'**,* *'PERLIN_NEW'**,* *'VORONOI_F1'**,* *'VORONOI_F2'**,* *'VORONOI_F3'**,* *'VORONOI_F4'**,* *'VORONOI_F2F1'**,* *'VORONOI_CRACKLE'**,* *'CELLNOISE'**]**.*) – A noise basis string.

    Returns:
    :   The noise vector.

    Return type:
    :   [`mathutils.Vector`](mathutils.html#mathutils.Vector "mathutils.Vector")

mathutils.noise.random()
:   Returns a random number in the range [0, 1).

    Returns:
    :   The random number.

    Return type:
    :   float

mathutils.noise.random_unit_vector(*\**, *size=3*)
:   Returns a unit vector with random entries.

    Parameters:
    :   **size** (*int*) – The size of the vector to be produced, in the range [2, 4].

    Returns:
    :   The random unit vector.

    Return type:
    :   [`mathutils.Vector`](mathutils.html#mathutils.Vector "mathutils.Vector")

mathutils.noise.random_vector(*\**, *size=3*)
:   Returns a vector with random entries in the range (-1, 1).

    Parameters:
    :   **size** (*int*) – The size of the vector to be produced.

    Returns:
    :   The random vector.

    Return type:
    :   [`mathutils.Vector`](mathutils.html#mathutils.Vector "mathutils.Vector")

mathutils.noise.ridged_multi_fractal(*position*, *H*, *lacunarity*, *octaves*, *offset*, *gain*, */*, *\**, *noise_basis='PERLIN_ORIGINAL'*)
:   Returns ridged multifractal value from the noise basis at the specified position.

    Parameters:
    :   - **position** ([`mathutils.Vector`](mathutils.html#mathutils.Vector "mathutils.Vector")) – The position to evaluate the selected noise function.
        - **H** (*float*) – The fractal dimension of the roughest areas.
        - **lacunarity** (*float*) – The gap between successive frequencies.
        - **octaves** (*int*) – The number of different noise frequencies used.
        - **offset** (*float*) – The height of the terrain above ‘sea level’.
        - **gain** (*float*) – Scaling applied to the values.
        - **noise_basis** (*Literal**[**'BLENDER'**,* *'PERLIN_ORIGINAL'**,* *'PERLIN_NEW'**,* *'VORONOI_F1'**,* *'VORONOI_F2'**,* *'VORONOI_F3'**,* *'VORONOI_F4'**,* *'VORONOI_F2F1'**,* *'VORONOI_CRACKLE'**,* *'CELLNOISE'**]**.*) – A noise basis string.

    Returns:
    :   The ridged multifractal value.

    Return type:
    :   float

mathutils.noise.seed_set(*seed*, */*)
:   Sets the random seed used for random_unit_vector, and random.

    Parameters:
    :   **seed** (*int*) – Seed used for the random generator.
        When seed is zero, the current time will be used instead.

mathutils.noise.turbulence(*position*, *octaves*, *hard*, */*, *\**, *noise_basis='PERLIN_ORIGINAL'*, *amplitude_scale=0.5*, *frequency_scale=2.0*)
:   Returns the turbulence value from the noise basis at the specified position.

    Parameters:
    :   - **position** ([`mathutils.Vector`](mathutils.html#mathutils.Vector "mathutils.Vector")) – The position to evaluate the selected noise function.
        - **octaves** (*int*) – The number of different noise frequencies used.
        - **hard** (*bool*) – Specifies whether returned turbulence is hard (sharp transitions) or soft (smooth transitions).
        - **noise_basis** (*Literal**[**'BLENDER'**,* *'PERLIN_ORIGINAL'**,* *'PERLIN_NEW'**,* *'VORONOI_F1'**,* *'VORONOI_F2'**,* *'VORONOI_F3'**,* *'VORONOI_F4'**,* *'VORONOI_F2F1'**,* *'VORONOI_CRACKLE'**,* *'CELLNOISE'**]**.*) – A noise basis string.
        - **amplitude_scale** (*float*) – The amplitude scaling factor.
        - **frequency_scale** (*float*) – The frequency scaling factor

    Returns:
    :   The turbulence value.

    Return type:
    :   float

mathutils.noise.turbulence_vector(*position*, *octaves*, *hard*, */*, *\**, *noise_basis='PERLIN_ORIGINAL'*, *amplitude_scale=0.5*, *frequency_scale=2.0*)
:   Returns the turbulence vector from the noise basis at the specified position.

    Parameters:
    :   - **position** ([`mathutils.Vector`](mathutils.html#mathutils.Vector "mathutils.Vector")) – The position to evaluate the selected noise function.
        - **octaves** (*int*) – The number of different noise frequencies used.
        - **hard** (*bool*) – Specifies whether returned turbulence is hard (sharp transitions) or soft (smooth transitions).
        - **noise_basis** (*Literal**[**'BLENDER'**,* *'PERLIN_ORIGINAL'**,* *'PERLIN_NEW'**,* *'VORONOI_F1'**,* *'VORONOI_F2'**,* *'VORONOI_F3'**,* *'VORONOI_F4'**,* *'VORONOI_F2F1'**,* *'VORONOI_CRACKLE'**,* *'CELLNOISE'**]**.*) – A noise basis string.
        - **amplitude_scale** (*float*) – The amplitude scaling factor.
        - **frequency_scale** (*float*) – The frequency scaling factor

    Returns:
    :   The turbulence vector.

    Return type:
    :   [`mathutils.Vector`](mathutils.html#mathutils.Vector "mathutils.Vector")

mathutils.noise.variable_lacunarity(*position*, *distortion*, */*, *\**, *noise_type1='PERLIN_ORIGINAL'*, *noise_type2='PERLIN_ORIGINAL'*)
:   Returns variable lacunarity noise value, a distorted variety of noise, from noise type 1 distorted by noise type 2 at the specified position.

    Parameters:
    :   - **position** ([`mathutils.Vector`](mathutils.html#mathutils.Vector "mathutils.Vector")) – The position to evaluate the selected noise function.
        - **distortion** (*float*) – The amount of distortion.
        - **noise_type1** (*Literal**[**'BLENDER'**,* *'PERLIN_ORIGINAL'**,* *'PERLIN_NEW'**,* *'VORONOI_F1'**,* *'VORONOI_F2'**,* *'VORONOI_F3'**,* *'VORONOI_F4'**,* *'VORONOI_F2F1'**,* *'VORONOI_CRACKLE'**,* *'CELLNOISE'**]**.*) – A noise type string.
        - **noise_type2** (*Literal**[**'BLENDER'**,* *'PERLIN_ORIGINAL'**,* *'PERLIN_NEW'**,* *'VORONOI_F1'**,* *'VORONOI_F2'**,* *'VORONOI_F3'**,* *'VORONOI_F4'**,* *'VORONOI_F2F1'**,* *'VORONOI_CRACKLE'**,* *'CELLNOISE'**]**.*) – A noise type string.

    Returns:
    :   The variable lacunarity noise value.

    Return type:
    :   float

mathutils.noise.voronoi(*position*, */*, *\**, *distance_metric='DISTANCE'*, *exponent=2.5*)
:   Returns a list of distances to the four closest features and their locations.

    Parameters:
    :   - **position** ([`mathutils.Vector`](mathutils.html#mathutils.Vector "mathutils.Vector")) – The position to evaluate the selected noise function.
        - **distance_metric** (*Literal**[**'DISTANCE'**,* *'DISTANCE_SQUARED'**,* *'MANHATTAN'**,* *'CHEBYCHEV'**,* *'MINKOVSKY'**,* *'MINKOVSKY_HALF'**,* *'MINKOVSKY_FOUR'**]**.*) – A distance metric string.
        - **exponent** (*float*) – The exponent for Minkowski distance metric.

    Returns:
    :   A list of distances to the four closest features and their locations.

    Return type:
    :   list[list[float] | list[[`mathutils.Vector`](mathutils.html#mathutils.Vector "mathutils.Vector")]]