Random simulations of lattice percolation

A simple demo of a quib-based GUI for lattice percolation.

• Features

  • User-defined functions

  • Random quibs

  • Graphics-driven assignments

• Try me

  • Try adjusting the lattice density. Note the size of the largest cluster (in gray).

from pyquibbler import iquib, initialize_quibbler, quiby, reset_random_quibs
initialize_quibbler()

import matplotlib.pyplot as plt
import numpy as np
from matplotlib.widgets import Slider, Button
from matplotlib.cm import get_cmap
from matplotlib.colors import ListedColormap
from scipy.ndimage import label
%matplotlib tk

@quiby
def get_connected_components(img):
    clusters, num_clusters = label(img)
    cluster_sizes, _ = np.histogram(clusters, np.arange(1, num_clusters + 2))
    largest_cluster = np.argmax(cluster_sizes) + 1
    cmp = get_cmap('rainbow', num_clusters + 1)
    cmp = cmp(np.arange(num_clusters + 1))
    cmp[0, :3] = 0
    cmp[largest_cluster, :3] = 0.7
    return clusters, ListedColormap(cmp)

# Set quibs
density = iquib(0.6)
size = iquib(200)
lattice = np.random.rand(size, size) < density
clusters, cmp = get_connected_components(lattice)

fig = plt.figure(figsize=(8, 8))
plt.imshow(clusters, cmap=cmp)
plt.axis('off');

# Slider for the density value
ax = fig.add_axes([0.3, 0.06, 0.4, 0.02])
Slider(ax, label='density = ', valmin=0, valmax=1, valinit=density);

# Randomization button
ax = fig.add_axes([0.75, 0.02, 0.2, 0.03])
randomize_button = Button(ax, label='Randomize')
randomize_button.on_clicked(lambda _: reset_random_quibs());