From Werner KRAUTH

This page presents the program markov_disks_box.py, a Markov-chain algorithm for four disks in a square box of sides 1.

Description

Program

import random

L = [[0.25, 0.25], [0.75, 0.25], [0.25, 0.75], [0.75, 0.75]]
sigma = 0.15
sigma_sq = sigma ** 2
delta = 0.1
n_steps = 1000
for steps in range(n_steps):
    a = random.choice(L)
    b = [a[0] + random.uniform(-delta, delta), a[1] + random.uniform(-delta, delta)]
    min_dist = min((b[0] - c[0]) ** 2 + (b[1] - c[1]) ** 2 for c in L if c != a)
    box_cond = min(b[0], b[1]) < sigma or max(b[0], b[1]) > 1.0 - sigma
    if not (box_cond or min_dist < 4.0 * sigma ** 2):
        a[:] = b
print L

Version

See history for version information.