PRNG Models Simulator

An educational web application that demonstrates how pseudo-random numbers are generated using three classical algorithms:

Si quieres ver la demo, puedes verla aquí: https://random-forge.vercel.app/

• Linear Congruential Generator (LCG)
• Multiplicative Congruential Generator (MCG)
• Middle-Square Method

---

📐 Algorithms

Linear Congruential Generator (LCG)

X(n+1) = (a × X(n) + c) mod m

Parameters: seed X₀, multiplier a, increment c, modulus m. Produces a sequence with period up to m. For maximum period, Hull–Dobell conditions must hold.

Multiplicative Congruential Generator (MCG)

X(n+1) = (a × X(n)) mod m

Special case of LCG with c = 0. The seed must be non-zero and co-prime with m. When m = 2³¹ − 1 (Mersenne prime) and a is a primitive root mod m, the period is m − 1.

Middle-Square Method

1. Start with a d-digit seed.
2. Square it and zero-pad to 2d digits.
3. Extract the middle d digits as the next value.
4. Repeat.

Proposed by John von Neumann (1946). Historically significant but prone to degenerating sequences.

---

🗂️ Project Structure

prng-models-simulator/
├── backend/
│   ├── app.py                  # Flask application + REST API
│   ├── requirements.txt
│   ├── tests.py                # Pytest test suite
│   └── generators/
│       ├── __init__.py
│       ├── lcg.py              # LCG algorithm
│       ├── mcg.py              # MCG algorithm
│       └── middle_square.py    # Middle-Square algorithm
└── frontend/
    ├── src/
    │   ├── App.jsx             # Main application component
    │   ├── App.css
    │   └── components/
    │       ├── MethodSelector.jsx   # Choose generator
    │       ├── Controls.jsx         # Parameter inputs
    │       ├── FormulaPanel.jsx     # Formula & explanation
    │       ├── ResultTable.jsx      # Step-by-step table
    │       └── SequenceChart.jsx    # Visualizations (Recharts)
    ├── package.json
    └── vite.config.js

---

🚀 Getting Started

Prerequisites

• Python 3.9+
• Node.js 18+

---

Backend

cd backend
pip install -r requirements.txt
python app.py

The Flask server starts at http://localhost:5000.

Run tests

cd backend
pip install pytest
pytest tests.py -v

---

Frontend

cd frontend
npm install
npm run dev

The React app starts at http://localhost:5173.

Make sure the backend is running first so the API calls succeed.

---

🔌 API Endpoints

All endpoints accept POST with a JSON body and return JSON.

POST /generate/lcg

{ "seed": 7, "a": 5, "c": 3, "m": 16, "count": 10 }

POST /generate/mcg

{ "seed": 7, "a": 5, "m": 16, "count": 10 }

POST /generate/middle-square

{ "seed": 1234, "iterations": 10 }

Response shape (all endpoints)

{
  "sequence":   [6, 1, 8, 11, 10],
  "normalized": [0.375, 0.0625, 0.5, 0.6875, 0.625],
  "steps": [
    {
      "iteration": 1,
      "x_prev": 7,
      "formula": "(5 × 7 + 3) mod 16",
      "x_next": 6,
      "normalized": 0.375
    }
  ]
}

---

📊 Example Inputs

Generator	Parameters	Expected first 5 values
LCG	X₀=7, a=5, c=3, m=16	6, 1, 8, 11, 10
MCG	X₀=7, a=5, m=16	3, 15, 11, 7, 3 ← cycle!
Middle-Square	seed=1234	5227, 3215, 3362, 3030, 1809

---

✨ Features

• Step-by-step table — shows each iteration with intermediate calculations
• Sequence plot — visualizes Uₙ over iterations
• Correlation plot — plots Uₙ vs Uₙ₊₁ to reveal patterns
• Cycle detection — warns when a value repeats (period discovered)
• Formula panel — explains the selected algorithm with parameters and examples