Monte-Carlo method for calculating Pi

montecarlo-pi.py

import pygame
import random
import math

# Initialize Pygame
pygame.init()

# Set up the screen
WIDTH, HEIGHT = 600, 600
screen = pygame.display.set_mode((WIDTH, HEIGHT))
pygame.display.set_caption("Monte Carlo Pi Approximation")

# Colors
BLACK = (0, 0, 0)
WHITE = (255, 255, 255)
RED = (255, 0, 0)
GREEN = (0, 255,0)
YELLOW = (0, 255, 255)

# Clock
clock = pygame.time.Clock()

# Number of points and points inside the circle
num_points = 0
points_inside_circle = 0

# Main loop
running = True
screen.fill(BLACK)
while running:
    for event in pygame.event.get():
        if event.type == pygame.QUIT:
            running = False

    # Generate random point
    x = random.uniform(0, 1)
    y = random.uniform(0, 1)

    # Draw points
    #pygame.draw.circle(screen, WHITE, (WIDTH // 2, HEIGHT // 2), WIDTH // 2, 1)  # Draw circle
    pygame.draw.arc(screen, WHITE, [-WIDTH,-HEIGHT,WIDTH*2,HEIGHT*2], math.radians(-90), math.radians(0),  1)
    pygame.draw.rect(screen, YELLOW, (0, 0, WIDTH, HEIGHT), 1)  # Draw square

    # Check if point is inside the circle
    distance = x**2 + y**2
    if distance <= 1:
        pygame.draw.circle(screen, RED, (int(x * WIDTH), int(y * HEIGHT)), 1)  # Draw random point
        points_inside_circle += 1
    else:
        pygame.draw.circle(screen, GREEN, (int(x * WIDTH), int(y * HEIGHT)), 1)  # Draw random points
    
    num_points += 1


    # Update display
    pygame.display.flip()

    # Limit frame rate
    #clock.tick(60)

    if num_points == 100000:
        running = False

# Calculate pi approximation
print(f"Points plotted {num_points}, {points_inside_circle} points inside circle")
pi_approximation = 4 * points_inside_circle / num_points
print("Approximation of Pi using Monte Carlo method:", pi_approximation)

# Quit Pygame
pygame.quit()