Julia Set Explorer

Multi-language fractal generator based on the Julia set with Python GUI, command-line interfaces, and Docker support.

Project Structure

Julia_Set/
├── rust/                   # Rust implementation (Docker-ready)
│   ├── src/
│   │   └── main.rs        # Main Rust source
│   ├── Cargo.toml         # Rust dependencies
│   └── Dockerfile         # Docker configuration
├── python/                # Python implementations
│   ├── julia.py          # Command-line interface
│   ├── julia_ui.py       # Interactive GUI
│   ├── requirements.txt  # Python dependencies
│   └── run_julia_ui.bat  # Windows launcher
├── c/                     # C implementation
│   └── julia.c
├── output/                # Generated images
├── docker-compose.yml     # Docker orchestration
├── run_docker.bat        # Windows Docker runner
├── run_docker.sh         # Unix Docker runner
└── README.md

Overview

This project provides tools to generate, explore, and animate beautiful Julia set fractals in multiple programming languages:

• Rust: High-performance, Docker-ready implementation with command-line arguments
• Python: Interactive GUI and command-line interface with advanced features
• C: Lightweight implementation for educational purposes

Features:

• High-performance calculation using optimized algorithms
• Interactive GUI for real-time parameter adjustments (Python)
• Command-line interface for batch processing
• Docker containerization for easy deployment
• Support for creating high-resolution images
• Animation capabilities for creating GIFs (Python)
• Parallel processing for maximum performance

How It Works

The Julia set is a fractal named after the French mathematician Gaston Julia. For each point (x,y) in the complex plane, the algorithm applies the formula z = z² + c repeatedly, where c is a complex constant. The number of iterations before z "escapes" (exceeds a certain value) determines the color of each pixel.

Command-Line Interface

The julia.py file can be executed from a terminal to generate Julia set images with various parameters:

GUI Interface

The project now features a full graphical interface (julia_ui.py) that allows for interactive exploration:

• Real-time updates when changing parameters
• Zoom and pan functionality
• Adjustable resolution, iterations, and colormaps
• Option to save images or create animations
• Calculation caching for improved performance

Examples

Different Resolutions

The same Julia set (c = -0.8 + 0.16j) at different resolutions:

Low resolution (100x100):

High resolution (2000x2000):

Animations

The generator can create two types of animated GIFs:

1. Zoom Animation: Progressively zooms into a part of the fractal

2. Parameter Animation: Shows how changes to the complex constant c affect the fractal

Installation and Usage

Docker (Recommended)

See the Quick Start section above.

Rust (Native)

cd rust
cargo build --release
./target/release/julia_set --help

Python

1. Navigate to the python directory:

cd python

2. Install dependencies:

pip install -r requirements.txt

3. Run the applications:

# Command-line interface
python julia.py

# Graphical interface
python julia_ui.py

# Or on Windows
run_julia_ui.bat

C

cd c
gcc -o julia julia.c -lm
./julia

Performance Notes

• The implementation uses Numba for significant performance acceleration
• Calculations are cached to improve responsiveness when exploring
• Multi-core processing is utilized for maximum performance