import numpy as np
import matplotlib.pyplot as plt

def dots(nmax, a=None, rot=None):
    r3o2, to_rads = np.sqrt(3)/2., np.pi/180.
    if a == None: a = 1.0
    if rot == None: rot=0.0
    i = np.arange(-nmax, nmax+1)
    I, J = np.meshgrid(i, i)
    keep = np.abs(I+J) <= nmax
    I, J = [thing[keep].flatten() for thing in (I, J)]
    x, y = a*(I + 0.5*J), a*r3o2*J
    c, s = [f(to_rads*rot) for f in (np.cos, np.sin)]
    return x*c - y*s, y*c + x*s

rat = np.sqrt(13./7)

A = dots(12)
B, C = dots(10, rat, 5.209), dots(10, rat, 11.218)

plt.figure()
plt.subplot(1, 2, 1)
plt.scatter([0], [0], s=400, c='black', edgecolor='none')
plt.scatter(A[0], A[1], s=200, c='none', edgecolor='black')
plt.scatter(B[0], B[1], s=60, c='black', edgecolor='none')
plt.xlim(-0.5, 14)
plt.ylim(-0.5, 14)
plt.gca().set_aspect('equal')
plt.title('(5, 6) <-> (5, 3) (5.209 deg)', fontsize=16)

plt.subplot(1, 2, 2)
plt.scatter([0], [0], s=400, c='black', edgecolor='none')
plt.scatter(A[0], A[1], s=200, c='none', edgecolor='black')
plt.scatter(C[0], C[1], s=60, c='black', edgecolor='none')
plt.xlim(-0.5, 14)
plt.ylim(-0.5, 14)
plt.gca().set_aspect('equal')
plt.title('(6, 5) <-> (5, 3) (11.218 deg)', fontsize=16)

plt.show()