FreeAeon-Fractal 1.0.1

Toolkit for Multifractal Analysis

FreeAeon-Fractal

The first GPU-accelerated version of the image-based multifractal analysis package for computing Multifractal Spectra, Fractal Dimensions, Local Multifractal $\alpha$-map, Fractal Lacunarity and Fourier Spectra of images or series. 🔗 More

Key Features

• 🎯 Multifractal Spectrum Analysis: Supports 2D images and 1D time series
• 📏 Fractal Dimension Calculation: BC, DBC, and SDBC methods
• 🔍 Lacunarity Analysis: Quantify spatial heterogeneity
• 🌊 Fourier Analysis: Frequency domain analysis and filtering
• ⚡ GPU Acceleration: Optional GPU support for faster computation
• 📊 Visualization: Built-in rich visualization capabilities

Application Domains

Medical Imaging

• Tissue Complexity: Quantify tissue structure via fractal dimension
• Heterogeneity Analysis: Reveal lesion characteristics via multifractal spectrum
• Texture Classification: Image classification based on fractal features

Materials Science

• Surface Morphology: Describe surface roughness via fractal dimension
• Porous Structure: Analyze internal structure via lacunarity
• Fracture Analysis: Identify fracture patterns via multifractal features

Financial Analysis

• Price Fluctuations: Analyze stock prices via multifractal spectrum
• Risk Assessment: Quantify risk based on fractal features
• Market Prediction: Long-range correlation analysis

Earth Sciences

• Terrain Analysis: Describe terrain complexity via fractal dimension
• Vegetation Distribution: Quantify vegetation coverage via lacunarity
• Climate Series: Multifractal analysis of time series

Image Processing

• Texture Classification: Texture recognition based on fractal features
• Image Segmentation: ROI extraction based on multifractal analysis
• Quality Assessment: Image complexity evaluation

📦 Installation

Install via pip:

pip install FreeAeon-Fractal

💡 Requires Python 3.6+ and OpenCV (cv2) support.

🖼 Usage

Get sample code

git clone https://github.com/jim-xie-cn/FreeAeon-Fractal.git
cd FreeAeon-Fractal

Calculate the Multifractal Spectrum of an image

python demo.py --mode mfs --image ./images/face.png

Example:

Calculate the Fractal Dimensions (Box-Counting, DBC, SDBC) of an image

python demo.py --mode fd --image ./images/face.png

Example:

Calculate the Local Multifractal $\alpha$-map of an image

python demo.py --mode alpha --image ./images/face.png

Example:

Lacunarity analysis of an image

python demo.py --mode=lacunarity --image=./images/fractal.png

Example:

Fourier analysis of an image

python demo.py --mode fourier --image ./images/face.png

Example:

Calculate the Multifractal Spectrum of a Series

python demo.py --mode series

Example:

Parameters

• --image: Path to the input image
• --mode: Analysis mode:
  • fd – Fractal Dimension
  • mfs – Multifractal Spectrum (default)
  • alpha – Local Multifractal $\alpha$-map
  • lacunarity - Lacunarity analysis
  • fourier - Fourier analysis
  • series - Multifractal Spectrum for Series analysis

Use GPU to speed up

from FreeAeonFractal.FAImageFDGPU import CFAImageFDGPU as CFAImageFD
from FreeAeonFractal.FAImageMFSGPU import CFAImageMFSGPU as CFAImageMFS
from FreeAeonFractal.FAImageLACGPU import CFAImageLACGPU as CFAImageLAC

📚 User Guide

See the following for complete usage, parameter details, and advanced examples:

Guide (Markdown) - 🐙 [GitHub View]

💡 Best for viewing directly on GitHub.

🔗 English Edition 🔗 Chinese Edition

Guide (HTML) - 🌐 [Browser View]

💡 Recommended for direct reading in browser.

🔗 English Edition 🔗 Chinese Edition

📁 Directory Structure

FreeAeon-Fractal/
├── FreeAeonFractal/      # Core module
│   ├── FAImageMFS.py     # 2D multifractal spectrum
│   ├── FAImageMFSGPU.py  # 2D multifractal spectrum (GPU)
│   ├── FASeriesMFS.py    # 1D multifractal spectrum
│   ├── FAImageFD.py      # Fractal dimension
│   ├── FAImageFDGPU.py   # Fractal dimension (GPU)
│   ├── FAImageLAC.py     # Lacunarity
│   ├── FAImageLACGPU.py  # Lacunarity (GPU)
│   ├── FAImageFourier.py # Fourier analysis
│   ├── FAImage.py        # Image utilities
│   ├── FASample.py       # Fractal sample generator
│   └── FAVisual.py       # Visualization tools
├── demo.py               # CLI interface
├── images/               # Example images
├── requirements.txt
├── setup.py
└── README.md

📄 License

This project is licensed under the MIT License. See LICENSE for details.

✍️ Author

Jim Xie

📧 E-Mail: [e-mail], [e-mail]

🔗 GitHub: https://github.com/jim-xie-cn/FreeAeon-Fractal

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🧠 Citation

If you use this project in academic work, please cite it as:

Jim Xie, FreeAeon-Fractal: A Python Toolkit for Fractal and Multifractal Image Analysis, 2025.
GitHub Repository: https://github.com/jim-xie-cn/FreeAeon-Fractal