Cyclic noise from filtering white noise in Python

readme.md

This generates cyclic/repeating/perfect loop noise by low-pass filtering white noise in a cyclic way. Useful for "random" but looping animations, etc.:

This one loops in both space and time, for instance:

Simplex noise typically has a more trapezoidal value distribution:

lmas/opensimplex#18 (comment)

which could be emulated by stretching the sample values.

Other examples:

• https://i.imgur.com/NGjfoOD.mp4
• https://i.imgur.com/eFES1QO.mp4
• https://i.imgur.com/MXWKOi6.png

[This code is a mess. TODO: Turn it into a def cyclic_noise function.]

cyclic_noise.py

import numpy as np
import matplotlib.pyplot as plt
from scipy.ndimage import gaussian_filter

rng = np.random.default_rng()

# shape = (1024, )
# shape = (512, 512)
shape = (128, 128, 128)

white = rng.normal(size=shape)
if len(shape) == 1:
    fig, ax = plt.subplots(3, 1, sharex='col',
                           num='LPF noise comparison',
                           figsize=(9, 6))
else:
    fig, ax = plt.subplots(1, 3,
                           num='LPF noise comparison',
                           figsize=(9, 6))

if white.ndim == 1:
    # Plot the curve
    ax[0].plot(white)
elif white.ndim == 2:
    # Plot a heatmap
    ax[0].imshow(white, cmap='gray')
elif white.ndim == 3:
    # Plot a heatmap of the first slice
    ax[0].imshow(white[0], cmap='gray')
ax[0].set_title('White noise')

filtered = gaussian_filter(white, 7, mode='wrap')

del white


# Plot it tiled next to itself
tiled = np.hstack((filtered, filtered))

if tiled.ndim == 1:
    ax[1].plot(tiled)
elif tiled.ndim == 2:
    ax[1].imshow(tiled, cmap='gray')
elif tiled.ndim == 3:
    ax[1].imshow(tiled[0], cmap='gray')
ax[1].set_title('Filtered, tiled')

del tiled

vmin = filtered.min()
vmax = filtered.max()
if filtered.ndim == 3:
    for n, slice in enumerate(filtered):
        plt.imsave(f'slice {n:03d}.png', filtered[n], vmin=vmin, vmax=vmax,
                   cmap='gray')

import numpy as np
from scipy.ndimage import gaussian_filter

def cyclic_noise(shape, sigma=7, rng)=None:
    """
shape stuff copy

sigmascalar or sequence of scalars

    Standard deviation for Gaussian kernel. The standard deviations of the Gaussian filter are given for each axis as a sequence, or as a single number, in which case it is equal for all axes.


copy rng stuff from scipy functions
    """
    white = rng.normal(size=shape)
    filtered = gaussian_filter(white, sigma, mode='wrap')
    return filtered