LCG Visualizer

A WPF application that visualizes the Linear Congruential Generator (LCG) algorithm.

📋 Overview

LCG (Linear Congruential Generator) is one of the pseudorandom number generation algorithms that uses the following formula:

X_{n+1} = (a × X_n + c) mod m

Where:

• X_n: Current value
• a: Multiplier
• c: Increment
• m: Modulus

This application visualizes the sequence generated by the LCG algorithm in a circular graph, allowing intuitive observation of cycle patterns.

✨ Key Features

• Real-time Visualization: Animated display of LCG sequence generation process
• Cycle Detection: Automatic detection of sequence periods and cycle starting points
• Parameter Adjustment: Free modification of m, a, c, seed values to observe various patterns
• Fullscreen Mode: Optimized visualization experience
• Color Gradients: Color coding for easy distinction between steps

🚀 Usage

System Requirements

• .NET 10.0 or higher
• Windows OS
• WPF-supported environment

Parameter Configuration

1. m (Modulus): Range of numbers to generate (positive integer)
2. a (Multiplier): Multiplier value
3. c (Increment): Increment value
4. seed: Initial value

Recommended Parameter Combinations

Parameter selection guide for good periods:

• m: Desired random number range
• a: (a-1) must be divisible by all prime factors of m
• c: Value coprime with m (1 recommended)

Example Combinations:

m=9, a=4, c=1, seed=0  (default)
m=16, a=5, c=1, seed=0
m=32, a=5, c=1, seed=0

Controls

1. Enter desired parameter values in the top input fields
2. Click the ▶ button to start visualization
3. Use the X button to close the application

📊 Visualization Interpretation

Screen Layout

• Circular Arrangement: Numbers from 0 to m-1 arranged clockwise
• Arrows: Indicate transitions between each step
• Colors: Gradient colors applied for each step
• Red Circle: Marks the cycle starting point

Result Analysis

• Cycle Length: Period of sequence repetition
• Pre-cycle Length: Length before cycle begins
• Visual Patterns: Geometric patterns appearing in the circular graph

🛠️ Tech Stack

• Language: C#
• Framework: .NET 10.0, WPF
• UI: XAML
• Asynchronous Processing: Task/async-await

📁 Project Structure

LCG_Visualizer/
├── MainWindow.xaml          # UI Layout
├── MainWindow.xaml.cs       # Main logic and visualization
├── App.xaml                 # Application configuration
├── App.xaml.cs              # Application entry point
└── LCG_Visualizer.csproj    # Project file

📚 Understanding LCG Algorithm

Operating Principle

1. Start with initial seed value
2. Repeatedly apply the formula (a × X_n + c) mod m
3. Generated sequence eventually forms a cycle
4. Cycle length and pattern are determined by parameters

Practical Applications

• Random number generation in game development
• Simulation and modeling
• Cryptographic applications (simple forms)
• Mathematical education and research

🔧 Build and Run

Using Visual Studio:

1. Open the solution file (.slnx)
2. Press F5 for debug run or Ctrl+F5 for release run

Using Command Line:

cd LCG_Visualizer
dotnet build
dotnet run

📄 License

This project is open source and licensed under the MIT License.