Question

Modify the Monte Carlo simulation to plot points in the entire circle. You will have to adjust the calculated value of pi accordingly.

Answer 1

import random as rnd
from matplotlib import pyplot as plt


n = 2500 # number of iterations


ins_number = 0
inside_x = []
inside_y = []
outside_x = []
outside_y = []


for i in range(n):
    x = rnd.uniform(-1,1)
    y = rnd.uniform(-1,1)
    if pow(x, 2) + pow(y, 2) <= 1:
        inside_x += [x]
        inside_y += [y]
        ins_number += 1
    else:
        outside_x += [x]
        outside_y += [y]


pi = 4*ins_number/n
print(pi)


fig = plt.figure() 
plt.plot(inside_x, inside_y, "bo")   # blue o inside circle
plt.plot(outside_x, outside_y, "ro") # red o outside of circle
plt.savefig("plot.png")