monte_carlo_pi.py

import numpy as np
import matplotlib.pyplot as plt
import time as time

total_random_points = int(input("\nNumber of random points for Monte Carlo estimate value of PI?\n>"))

start_time = time.time()

inside_circle = 0

x_plot_array = np.empty(shape=(1, total_random_points))
y_plot_array = np.empty(shape=(1, total_random_points))

pi_approx = 0

for i in range(0, total_random_points):
    x = np.random.rand()
    x_plot_array = np.append(x_plot_array, [x])

    y = np.random.rand()
    y_plot_array = np.append(y_plot_array, [y])

    x_squared = x ** 2;
    y_squared = y ** 2;

    if np.sqrt(x_squared + y_squared) < 1.0:
        inside_circle += 1

    pi_approx = inside_circle / (i + 1) * 4

print(f"\nApproximate value for PI: {pi_approx}")
print(f"\nDifference to exact value of PI: {pi_approx - np.pi}")
print(f"Percent Error: (approx-exact)/exact*100: {(pi_approx-np.pi)/np.pi*100}%")
print(f"Execution Time: {time.time() - start_time} seconds\n")

# Draw plot

random_points_plot = plt.scatter(x_plot_array, y_plot_array, color='blue', s=0.1)
circle_plot = plt.Circle((0, 0), 1, color='red', linewidth=2, fill=False)

ax = plt.gca()
ax.cla()

ax.add_artist(random_points_plot)
ax.add_artist(circle_plot)

plt.show()