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)

fig, (ax1, ax2) = plt.subplots(1, 2, figsize=[12, 7.5])
ax1.scatter([0], [0], s=400, c='black', edgecolor='none')
ax1.scatter(A[0], A[1], s=200, c='none', edgecolor='black')
ax1.scatter(B[0], B[1], s=60, c='black', edgecolor='none')
ax1.set_xlim(-0.5, 14)
ax1.set_ylim(-0.5, 14)
ax1.set_aspect('equal')
for i, j in ((1,3), (2,6), (5,2), (9,1), (3,9), (-2, 7), (-1, 10), (-5, 11)):
    x0 = i + j * 0.5
    y0 = j * np.sqrt(3)/2
    ax1.scatter([x0], [y0], c = 'none', edgecolor='red', s=550, lw=2)
i, j = 6, 5
x0 = i + j * 0.5
y0 = j * np.sqrt(3)/2
d, dd = 2, 1.5
ax1.arrow(x0+d, y0+d, -dd, -dd, color='red', width=0.1, head_width=0.5, head_length=0.5)
ax1.set_title('(' + str(i) + ',  '+ str(j) + ') <-> (5, 3) (5.209°)', fontsize=16)

ax2.scatter([0], [0], s=400, c='black', edgecolor='none')
ax2.scatter(A[0], A[1], s=200, c='none', edgecolor='black')
ax2.scatter(C[0], C[1], s=60, c='black', edgecolor='none')
ax2.set_xlim(-0.5, 14)
ax2.set_ylim(-0.5, 14)
ax2.set_aspect('equal')
for i, j in ((-6, 11), ):
    x0 = i + j * 0.5
    y0 = j * np.sqrt(3)/2
    ax2.scatter([x0], [y0], c = 'none', edgecolor='red', s=550, lw=2)
i, j = 5, 6
x0 = i + j * 0.5
y0 = j * np.sqrt(3)/2
d, dd = 2, 1.5
ax2.arrow(x0+d, y0+d, -dd, -dd, color='red', width=0.1, head_width=0.5, head_length=0.5)
ax2.set_title('(' + str(i) + ',  '+ str(j) + ') <-> (5, 3) (11.218°)', fontsize=16)
plt.subplots_adjust(left=0.1, right=0.9)
plt.show()