general

from math import sqrt
import numpy as np
import matplotlib.pyplot as plt

def centeredgen(L):
  for i in range(L+1):
    for j in range(L+1):
      for k in range(L+1):
        yield i,j,k
        if k > 0:
          yield i,j,-k
        if j > 0:
          yield i,-j,k
          if k > 0:
            yield i,-j,-k
        if i > 0:
          yield -i,j,k
          if k > 0:
            yield -i,j,-k
          if j > 0:
            yield -i,-j,k
            if k > 0:
              yield -i,-j,-k
        
if __name__ == "__main__":
  L = 30
  M = 0.0
  a = []
  gen = centeredgen(L)
  next(gen) # skip the 0,0,0
  sign2 = lambda n: " " if n >= 0 else ""
  sign = lambda n: " "*(3-len(str(n)))
  for i,j,k in gen:
      h = ((-1.0)**(i+j+k))/sqrt(i*i+j*j+k*k)
      M += h
      a += [M]
      print("%s%d,%s%d,%s%d -> %s%01.4f => %s%01.4f"%(sign(i),i,sign(j),j,sign(k),k,sign2(h),h,sign2(M),M))
      
  print("\nMean estimate: %.4f" % np.mean(a))
  plt.plot(a)
  plt.show()