I wrote two articles on my blog about this project, the first one is about the generation of 2D noise while the second one is about the generation of 3D noise, feel free to read them!

You can find implementations using numba here.

A fast and simple perlin noise generator using numpy.

You can install this package via:

pip3 install git+https://github.com/pvigier/perlin-numpy

from perlin_numpy import (
    generate_fractal_noise_2d, generate_fractal_noise_3d,
    generate_perlin_noise_2d, generate_perlin_noise_3d
)

The function generate_perlin_noise_2d generates a 2D texture of perlin noise. Its parameters are:

• shape: shape of the generated array (tuple of 2 ints)
• res: number of periods of noise to generate along each axis (tuple of 2 ints)
• tileable: if the noise should be tileable along each axis (tuple of 2 bools)

Note: shape must be a multiple of res

The function generate_fractal_noise_2d combines several octaves of 2D perlin noise to make 2D fractal noise. Its parameters are:

• shape: shape of the generated array (tuple of 2 ints)
• res: number of periods of noise to generate along each axis (tuple of 2 ints)
• octaves: number of octaves in the noise (int)
• persistence: scaling factor between two octaves (float)
• lacunarity: frequency factor between two octaves (float)
• tileable: if the noise should be tileable along each axis (tuple of 2 bools)

Note: shape must be a multiple of lacunarity^(octaves-1)*res

The function generate_perlin_noise_3d generates a 3D texture of perlin noise. Its parameters are:

• shape: shape of the generated array (tuple of 3 ints)
• res: number of periods of noise to generate along each axis (tuple of 3 ints)
• tileable: if the noise should be tileable along each axis (tuple of 3 bools)

Note: shape must be a multiple of res

The function generate_fractal_noise_2d combines several octaves of 3D perlin noise to make 3D fractal noise. Its parameters are:

• shape: shape of the generated array (tuple of 3 ints)
• res: number of periods of noise to generate along each axis (tuple of 3 ints)
• octaves: number of octaves in the noise (int)
• persistence: scaling factor between two octaves (float)
• lacunarity: frequency factor between two octaves (float)
• tileable: if the noise should be tileable along each axis (tuple of 3 bools)

Note: shape must be a multiple of lacunarity^(octaves-1)*res

Note these snippets require matplotlib.

import matplotlib.pyplot as plt
import numpy as np
from perlin_numpy import (
    generate_perlin_noise_2d, generate_fractal_noise_2d
)

np.random.seed(0)
noise = generate_perlin_noise_2d((256, 256), (8, 8))
plt.imshow(noise, cmap='gray', interpolation='lanczos')
plt.colorbar()

np.random.seed(0)
noise = generate_fractal_noise_2d((256, 256), (8, 8), 5)
plt.figure()
plt.imshow(noise, cmap='gray', interpolation='lanczos')
plt.colorbar()
plt.show()

import matplotlib.pyplot as plt
import matplotlib.animation as animation
import numpy as np
from perlin_numpy import generate_fractal_noise_3d

np.random.seed(0)
noise = generate_fractal_noise_3d(
    (32, 256, 256), (1, 4, 4), 4, tileable=(True, False, False)
)

fig = plt.figure()
images = [
    [plt.imshow(
        layer, cmap='gray', interpolation='lanczos', animated=True
    )]
    for layer in noise
]
animation_3d = animation.ArtistAnimation(fig, images, interval=50, blit=True)
plt.show()

import matplotlib.pyplot as plt
import matplotlib.animation as animation
import numpy as np
from perlin_numpy import generate_perlin_noise_3d

np.random.seed(0)
noise = generate_perlin_noise_3d(
    (32, 256, 256), (1, 4, 4), tileable=(True, False, False)
)

fig = plt.figure()
images = [
    [plt.imshow(
        layer, cmap='gray', interpolation='lanczos', animated=True
    )]
    for layer in noise
]
animation_3d = animation.ArtistAnimation(fig, images, interval=50, blit=True)
plt.show()