Naive surface 2d.py

From Werner KRAUTH

Context

This page is part of my 2024 Beg Rohu Lectures on "The second Markov chain revolution" at the Summer School "Concepts and Methods of Statistical Physics" (3 - 15 June 2024).

Python program

import random, math
import matplotlib.pyplot as plt
N_trials = 1000000
data = []
twopi = 2.0 * math.pi
for iter in range(N_trials):
    x = random.uniform(-1.0, 1.0)
    y = random.uniform(-1.0, 1.0)
    r = math.sqrt(x ** 2 + y ** 2)
    if r < 1.0:
        x = x / r; y = y / r # uniform sample on the surface of unit sphere
        phi = (math.atan2(y, x) + twopi) % twopi
        data.append(phi)
plt.title('naive_surface_2d.py (histogram of angles)')
plt.xlabel('angle')
plt.ylabel('histogram')
plt.hist(data, bins=100, density=True)
plt.show()