1.4. Appendix: Monte Carlo Pi Python¶

import random as r
import math as m
import matplotlib.pyplot as plt

from ipywidgets import interact, interactive, fixed, interact_manual
import ipywidgets as widgets

# Random Seed
r.seed(42)

def estimatePI(n_trials=10):

    
    successfulHits = 0
    circleRadius = 0.5
    squareLength = 1.0

    inside_x,inside_y=[],[]
    outside_x,outside_y=[],[]
    
    # Iterate for the number of darts.
    for i in range(0, n_trials):
        x=0 # Your CODE HERE 
        
        
    pi = 0 # Estimate Pi

    print(f"{pi:.10f}")

    fig, ax=plt.subplots(1, figsize=(5,5))

    ax.scatter(inside_x,inside_y)
    ax.scatter(outside_x,outside_y)

    plt.show()

The below code provides an interactive widget with a slider that will redraw the plot once you change the slider.

You can also simply run estimatePI(n_trials=100) to run the function once. If you struggle to generate the plot using the slider because of resource limitation, reduce the maximum of trials in the slider to max=10000 and calculate one estimation of \(\pi\) with a higher number of trials using the standalone function estimatePI(n_trials=SomeLargeNumber)

interact(estimatePI, n_trials=widgets.IntSlider(min=2, max=1000000, step=100, value=1000))

<function __main__.estimatePI(n_trials=10)>

Molecular Dynamics and Monte Carlo

1.4. Appendix: Monte Carlo Pi Python¶