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.

Contents 1 Description 2 Program 3 Version

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.

import random

neighbor =  [[1, 3, 0, 0], [2, 4, 0, 1], [2, 5, 1, 2],
             [4, 6, 3, 0], [5, 7, 3, 1], [5, 8, 4, 2],
             [7, 6, 6, 3], [8, 7, 6, 4], [8, 8, 7, 5]]
t_max = 4
N_runs = 25600
for run in range(N_runs):
    site = 8
    t = 0
    while t < t_max:
        t += 1
        site = neighbor[site][random.randint(0, 3)]
    print site