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# dmishin/coprime_fft.py

Created Oct 23, 2014
Generate Fourier transform of the coprime integers map
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 #Requires: numpy, PIL from fractions import gcd from numpy import array, meshgrid, frompyfunc, clip, histogram from numpy.fft import fft2 import numpy as np from PIL import Image def value_diapason(x, percent=0.95, nbins=100): """Use histogram to determine area, covering 95% of values""" counts, bins = histogram(x.ravel(),nbins) total = sum(counts) accum = 0 low = bins[-1] high = bins[0] for i, cnt in sorted( enumerate(counts), key = (lambda i_c: i_c[1]), reverse=True ): accum += cnt low = min(low, bins[i]) high = max(high, bins[i+1]) if accum > percent * total: break return low, high ############## Parameters ################# N = 2048 gamma = 1.9 output = r"coprime-fft.png" ############## Calculation ############### t = array(range(N), dtype=int) x,y = meshgrid(t,t) g = frompyfunc(gcd, 2, 1)(x,y) == 1 lfg = np.log(np.abs(fft2(g))) - np.log(N**2) low, high = value_diapason( lfg ) img = Image.fromarray( (clip((lfg-low)/(high-low),0,1)**gamma*255).astype(np.uint8), "P") img.save(output)