moiré

Generate moiré patterns from simple array ops.

All of the pattern generation logic is located in a single function, moire_pattern().

Usage

Parameters

• n int: Size of the image width and height in pixels (n x n).
• k float: Scaling factor affecting pattern frequency and density.
• kernel {'elliptical', 'hexagonal', 'radial', 'spiral', 'square', 'star', 'wave'} | Callable[[ndarray, ndarray], ndarray]: Determines pattern shape. Can be the name of a preset kernel or a callable object which accepts two arrays and returns an array.
• colorize bool: False for greyscale (default), True for RGB.

Preset Kernels

The global KERNELS dict provides a namespace for preset kernel functions.

• 'elliptical'
• 'hexagonal'
• 'radial'
• 'spiral'
• 'square'
• 'star'
• 'wave'

The presets offer quite a bit when it comes to experimentation.

This is especially true if one were to chain them together using higher-order lambdas, such as in the following code:

from moire import moire_pattern, KERNELS
from PIL import Image

# using the product of two other patterns as the pattern
kernel_chain = lambda x, y: KERNELS['hexagonal'](x, y) * KERNELS['star'](x, y)

output = moire_pattern(m=999, k=777, kernel=kernel_chain, colorize=True)

Image.fromarray(output).show()

... which creates this output image:

Example Usage

Using the 'spiral' preset kernel:

from moire import moire_pattern
from PIL import Image

output = moire_pattern(n=500, k=100.0, kernel='spiral')

Image.fromarray(output).show()

Using a custom kernel, with colorized output:

import numpy as np
from moire import moire_pattern
from PIL import Image

def custom_kernel(x, y):
    return np.sin(x) * np.cos(y)

output = moire_pattern(n=500, k=100.0, kernel=custom_kernel, colorize=True)

Image.fromarray(output).show()

Additional Resources

• Circle Squares fractal - the base implementation is pretty much directly from this. also very cool site, shoutout Paul Bourke fr
• 黎曼ζ函數 - mathematics wikipedia