Code for producing a figure showing dobble matrix

dobble.py

from itertools import combinations
import matplotlib.pyplot as plt
from matplotlib.patches import Rectangle
from matplotlib.text import Text

def dobble(p):
    cards = [[] for i in range(p**2 + p + 1)]
    cards[0].append(0)
    for i in range(p+1):
        for j in range(p):
            cards[1 + i*p + j].append(i)
            cards[i].append(1 + i*p + j)
    for i in range(p):
        for j in range(p):
            for k in range(p):
                cards[1 + p + i*p + k].append(1 + p + j*p + (i*j - k) % p)
    return cards

for card0, card1 in combinations(dobble(7), 2):
    assert len(set(card0) & set(card1)) == 1

def plot_dobble(p, bw=0.15):
    cards = dobble(p)
    n = p**2 + p + 1
    fig, ax = plt.subplots(figsize=(7,7), subplot_kw=dict(aspect='equal'))
    fig.subplots_adjust(0, 0, 1, 1)
    ax.set_xlim(-bw, n)
    ax.set_ylim(n, -bw)
    ax.axis('off')
    for i, card in enumerate(cards):
        for j in range(n):
            ax.add_patch(Rectangle((i, j), 1-bw, 1-bw, linewidth=0, color='k', alpha=0.5 if j in card else 0.1))
    def horiz(x0, x1, y, color):
        ax.add_patch(Rectangle((x0-bw, y-bw), x1-x0+2*bw, bw, linewidth=0, color=color))
    def vert(x, y0, y1, color):
        ax.add_patch(Rectangle((x-bw, y0-bw), bw, y1-y0+2*bw, linewidth=0, color=color))
    def rect(x, y, size, color):
        horiz(x, x+size, y, color)
        horiz(x, x+size, y+size, color)
        vert(x, y, y+size, color)
        vert(x+size, y, y+size, color)
    for i in range(p+1):
        for j in range(p+1):
            rect(1 + j*p, 1 + i*p, p, 'C2')
    rect(1+p, 1+p, p**2, 'C1')
    for i in range(p):
        for j in range(p):
            ax.add_artist(Text(1+(1.5+j)*p, 1+(1.5+i)*p, '$C_{{{},{}}}$'.format(i, j), ha='center', va='center', size='xx-large', family='serif'))
    return fig, ax

fig, ax = plot_dobble(5)
fig.savefig('/tmp/fig.png', dpi=628/10)