🌀 3D Fractal Explorer

An interactive 3D visualization tool for exploring Mandelbrot and Julia sets, built with Python, OpenGL, and PyQt5.

✨ Features

• 🎨 Real-time 3D visualization of fractals
• 🔄 Interactive rotation and zoom capabilities
• 🌈 Dynamic color animation
• 🔲 Support for both Mandelbrot and Julia sets
• 🎮 Intuitive GUI controls
• 🖱️ Mouse-based navigation
• ⚡ Optimized performance with OpenGL

🚀 Getting Started

Prerequisites

python 3.7+
PyQt5
PyOpenGL
numpy

Installation

1. Clone the repository:

git clone https://github.com/melihcanndemir/3d-fractal-explorer.git
cd 3d-fractal-explorer

2. Install dependencies:

pip install -r requirements.txt

3. Run the application:

python fractal_explorer.pyw

📖 Educational Content

What are Fractals?

Fractals are complex geometric patterns that repeat infinitely at different scales. They're created by repeating a simple mathematical process over and over.

The Mathematics Behind It

Mandelbrot Set

The Mandelbrot set is defined by the function:

z₍ₙ₊₁₎ = zₙ² + c

where z₀ = 0 and c is a complex number. A point c is in the Mandelbrot set if the sequence remains bounded.

Julia Set

Julia sets use the same function as the Mandelbrot set:

z₍ₙ₊₁₎ = zₙ² + c

but here, c is fixed and z₀ varies. Each different value of c creates a different Julia set.

🎮 How to Use

1. Basic Navigation:

   • 🖱️ Left-click and drag to move around
   • 🖲️ Mouse wheel to zoom in/out
   • 🔄 Watch the automatic rotation

2. Controls:

   • Switch between Mandelbrot and Julia sets
   • Adjust iteration count for detail
   • Modify Julia set parameters
   • Control color animation speed

🔧 Technical Implementation

The project demonstrates several advanced programming concepts:

• 3D Graphics Programming with OpenGL
• Complex Number Mathematics
• Real-time Animation
• Event-driven Programming
• GUI Development with Qt
• Performance Optimization

Key Components

# Example of the core fractal calculation
def calculate_fractal(z, c, max_iter):
    n = 0
    while abs(z) <= 2 and n < max_iter:
        z = z*z + c
        n += 1
    return n

🤝 Contributing

Contributions are welcome! Here are ways you can contribute:

• 🐛 Report bugs
• ✨ Propose new features
• 📝 Improve documentation
• 🔍 Submit pull requests

📚 Learning Resources

To learn more about the concepts used in this project:

• Fractal Mathematics
• OpenGL Tutorial
• PyQt5 Documentation
• Complex Numbers in Python

📄 License

This project is licensed under the MIT License - see the LICENSE file for details.

🌟 Acknowledgments

• Thanks to Benoit B. Mandelbrot for his groundbreaking work on fractals
• PyQt and OpenGL communities for their excellent documentation
• All contributors and users of this project

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Made with ❤️ by Melih Can Demir

"The beauty of fractals shows that simple rules can create infinite complexity."