Fractal Dimension and Clinical Neurophysiology: Code Repository

This repository contains the Python scripts and related resources used in the paper:

"Fractal dimension and clinical neurophysiology fusion to gain a deeper brain signal understanding: a Systematic Review"

The scripts generate the figures presented in the paper, providing insights into fractal dimension (FD) estimation methods, their applications, and step-by-step visualizations of key methodologies.

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Repository Structure

File Name	Description
Koch_Curve.py	Generates the Koch Curve, demonstrating fractal properties visually.
Koch_Snowflakes.py	Generates Koch Snowflakes, another fractal structure highlighting self-similarity.
Menger_Sponge.py	Creates the Menger Sponge, a 3D fractal model.
Sierpinski_Triangle.py	Generates the Sierpinski Triangle, a classic 2D fractal example.
Stationary_vs_Non_Stationary.py	Provides visualizations distinguishing stationary and non-stationary signals, relevant for fractal analysis.
fGn_fBm_TLK_wsc.py	Simulates fractional Gaussian noise (fGn) and fractional Brownian motion (fBm), and computes their respective properties.
functions_Comparative.py	Contains functions for comparing various FD estimation methods, used in main_Comparative.py.
main_Comparative.py	Generates a figure comparing FD estimation methods for different signal types (STS, WCF, TLF, fBm, fGn) using methods like sPSD, DFA, HE, HFD, and KFD.
functions_Higuchi.py	Implements helper functions for understanding Higuchi’s FD method, used in main_Higuchi.py.
main_Higuchi.py	Generates step-by-step visualizations of Higuchi’s FD method.
README.md	Provides an overview of the repository, code instructions, and file descriptions.

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Key Figures

1. Comparison of FD Estimation Methods (Generated by main_Comparative.py)

This figure compares various FD estimation methods across multiple signal types (STS).

• Dashed Black Line: Represents the ideal scenario where estimated FD matches theoretical FD ((FD_{th})).
• Gray Area: Highlights the typical FD range (1 to 2) for time series.
• Extended Axis Limits: Visualize methods exceeding this range.

The results include methods like sPSD, DFA, HE, HFD, and KFD applied to WCF, TLF, fBm, and fGn.

2. Understanding Higuchi’s Method (Generated by main_Higuchi.py)

Figures illustrate the step-by-step process of Higuchi’s FD method, offering an intuitive understanding of its application and significance.

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Sample Output from fGn_fBm_TLK_wsc.py:

Sample Output from Stationary_vs_Non_Stationary.py:

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How to Run the Code

1. Clone the repository:

   git clone https://github.com/BrainLabUnit/Fractal-dimension-and-clinical-neurophysiology.git
   cd Fractal-dimension-and-clinical-neurophysiology