import numpy as np
from PIL import Image

nperiods =   21                                   # number of periods
size     = 1000                                   # size of square image

# waveform: any function with arguments and return values in [0..1]

waveform = lambda u: 2 * np.where(u<0.5, u, 1-u)  # triangle
# waveform = lambda u: np.where(u<0.5, 0, 1)      # rectangle
# waveform = lambda u: u                          # sawtooth
# waveform = lambda u: (np.sin(2*pi*u) + 1) / 2   # sine

def mapping(y, x):
  u = nperiods * np.arctan2(y - size/2, x - size/2) / (2*np.pi) % 1
  return np.uint16(0xffff * waveform(u) + 0.5)

array = np.fromfunction(mapping, (size, size), dtype=np.uint16)
Image.fromarray(array).save(f'muster-{nperiods}-{size}.png')