Monte Carlo Pi Estimation

monto.carlo.mp4

Project Description

This project visualizes the process of estimating the value of Pi using the Monte Carlo method. It uses random point generation within a square that bounds a circle to approximate Pi.

The visualization includes:

• Red points: Represent points inside the circle.
• Green points: Represent points outside the circle.
• A progress bar: Displays the simulation progress.
• Real-time updates: Shows the current Pi estimate and error rate compared to the true value of π.

---

How It Works

The Algorithm

1. Initialize circle_points, square_points, and interval to 0.
2. Generate a random point x.
3. Generate a random point y.
4. Calculate ( d = x * x + y * y ).
5. If ( d <= 1 ), increment circle_points.
6. Increment square_points.
7. Increment interval.
8. If interval < NO_OF_ITERATIONS, repeat from step 2.
9. Calculate pi = 4 * (circle_points / square_points).
10. Terminate.

Features

1. Dynamic Point Generation:
   • Points are randomly generated and drawn in batches for efficiency.
2. Interactive Visualization:
   • Displays points on a canvas in real-time.
3. Progress Feedback:
   • A progress bar tracks the completion percentage of the simulation.
4. Real-Time Insights:
   • Displays the estimated Pi value and the error rate dynamically.

Technologies Used

• HTML5: For structuring the page and creating the canvas element.
• CSS3: For styling the visualization and progress bar.
• JavaScript: For implementing the Monte Carlo algorithm and visualization logic.

Usage

1. Clone or download the repository.
2. Open the index.html file in any modern browser.
3. Click the "Start Simulation" button to begin.
4. Observe:
   • The canvas updates with red and green points.
   • The progress bar indicates the simulation progress.
   • Real-time Pi estimate and error rate updates.

Key Achievements

• Approximated the value of Pi using 1,000,000 random points.
• Achieved an estimated value of Pi close to 3.1412, with a minimal error rate.
• Created an interactive and educational visualization of Pi estimation.