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https://github.com/shreyasmehta05/prng

A Python-based pseudo-random number generator and Monte Carlo simulation for estimating π with visualization.
https://github.com/shreyasmehta05/prng

Last synced: about 1 month ago
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A Python-based pseudo-random number generator and Monte Carlo simulation for estimating π with visualization.

Host: GitHub
URL: https://github.com/shreyasmehta05/prng
Owner: shreyasMehta05
Created: 2024-12-08T09:03:03.000Z (about 2 months ago)
Default Branch: main
Last Pushed: 2024-12-08T09:20:20.000Z (about 2 months ago)
Last Synced: 2024-12-08T10:20:46.317Z (about 2 months ago)
Language: Python
Homepage:
Size: 623 KB
Stars: 0
Watchers: 1
Forks: 0
Open Issues: 0
Metadata Files:
- Readme: README.md

Awesome Lists containing this project

README

# **PRNG** - A Pseudo-Random Number Generator in Python 🧮✨
![Waketime](https://img.shields.io/badge/Waketime-5%20hrs%2002%20minutes-blueviolet?style=plastic)

This project implements a **Pseudo-Random Number Generator (PRNG)** in Python3. It uses a middle-square method to generate pseudo-random numbers and includes a Monte Carlo simulation for estimating π. The results are visualized using `matplotlib`.
- This Project was part of the course `Introduction to Software Systems` at **IIIT Hyderabad**.
---

## **📜 Project Overview**

### **✨ Main Features**
- **🛠️ Custom Pseudo-Random Number Generator:**
A deterministic approach to generating pseudo-random numbers with user-defined seed and iterations.
- **📊 Monte Carlo Simulation for π Estimation:**
Uses generated pseudo-random numbers to estimate the value of π.
- **📈 Visualization:**
Frequency distribution of random numbers and error analysis in π estimation.

---

## **📂 Directory Structure**
```
PRNG/
├── estimation_of_pie.png # 📊 Graph: Error in π estimation
├── estimation_of_pie.py # 🧮 Monte Carlo π estimation script
├── estimation_of_pi_improved.png # 📈 Improved graph: Error in π estimation
├── Final_results.png # 🏁 Final Estimation Result
├── pseudo_random_generator.py # 🎲 PRNG implementation
├── README.md # 📖 Documentation file
└── __pycache__/ # ⚙️ Compiled Python files
```

---

## **🚀 How to Run**

### **1️⃣ Clone the Repository**
```bash
git clone https://github.com/shreyasMehta05/PRNG.git
cd PRNG
```

### **2️⃣ Install Required Libraries**
Ensure you have Python 3 installed. Install the dependencies using:
```bash
pip install matplotlib
```

### **3️⃣ Run the Pseudo-Random Generator**
Generate and visualize a frequency distribution of pseudo-random numbers:
```bash
python3 pseudo_random_generator.py
```

### **4️⃣ Estimate π Using Monte Carlo Simulation**
Estimate the value of π using the generated pseudo-random numbers:
```bash
python3 estimation_of_pie.py
```

---

## **🎲 Pseudo-Random Generator (`pseudo_random_generator.py`)**

This script generates `k` pseudo-random numbers using the middle-square method.

### **⚙️ Usage**
- Input the **number of digits** for the seed.
- Input the **number of random numbers** to generate.

### **🔑 Key Functionality**
- **`pseudoRandNumGen(seed, k)`**:
Generates a list of `k` pseudo-random numbers based on the given seed.
- **📊 Visualization:**
Outputs a histogram of the random number distribution.

---

## **📊 Monte Carlo Simulation for π Estimation (`estimation_of_pie.py`)**

This script estimates the value of π using the Monte Carlo method. It compares two approaches:
1. **Custom Pseudo-Random Number Generator** (`PRNG`).
2. **Python’s Built-in Random Library** (`random`).

### **✨ Key Features**
- **📐 Monte Carlo Algorithm:**
Uses random points within a square to calculate π.
- **📈 Visualization:**
- Error in π estimation using custom PRNG and Python's `random`.
- Relative error comparison.

---

## **📷 Visualization Examples**

### **1️⃣ Frequency Distribution of Pseudo-Random Numbers**
![Frequency Distribution](estimation_of_pie.png)
_Histogram showing the frequency distribution of generated random numbers._

### **2️⃣ Error in Estimation of π**
![Error in π Estimation](estimation_of_pi_improved.png)
_Comparison of errors using custom PRNG and Python’s `random`._

---

## **📋 Functions Overview**

### **`pseudo_random_generator.py`**
- **`numberOfDigits(n)`**:
Returns the number of digits in a given number.
- **`pseudoRandNumGen(seed, k)`**:
Core function to generate pseudo-random numbers using the middle-square method.

### **`estimation_of_pie.py`**
- **`generate(k)`**:
Generates two sets of pseudo-random numbers (`x` and `y`) for Monte Carlo simulation.
- **`inSquare(l)`**:
Maps generated points to a unit square.
- **`estimate_pi(l)`**:
Estimates π using points within a circle.
- **`estimate_pi_using_random(l)`**:
Estimates π using Python’s `random`.
- **`estimate_pi_error(l)`**:
Calculates the absolute error in π estimation.

---

## **📊 Results**
- **✅ Closest Estimate to π (Custom PRNG):**
Closest calculated value of π: **`3.141`**
- **📈 Visualization of Errors:**
Demonstrates the effectiveness of the custom PRNG compared to Python's built-in `random` library.
- **🏁 Final Results:**
![Final Results](Final_results.png)
---

## **📦 Dependencies**
- **🐍 Python 3**
- **📊 `matplotlib`** (for visualizations)

---

## **👨‍💻 Author**
- **Shreyas Mehta**

---