Computing Multifractal Spectrum

This MATLAB implementation provides a computational tool for estimating multifractal spectrum, which is a powerful method for analyzing self-similarity properties in complex signals. The algorithm employs box-counting methodology with appropriate scaling techniques to characterize multifractal dimensions across different singularity strengths. Multifractal analysis finds extensive applications across multiple disciplines including image processing (texture analysis, pattern recognition), seismology (earthquake wave propagation studies), and biomedical engineering (abnormal signal detection in EEG/ECG data, human gait analysis). The core implementation handles signal partitioning, probability measure calculation, and Legendre transformation to derive the multifractal spectrum. Key functions include automated scaling range selection, moment calculation for various q-values, and linear regression for dimension estimation. Researchers can utilize this program to analyze fractal characteristics in their datasets, detect anomalies in temporal patterns, and study scale-invariant properties in complex systems. The code structure allows straightforward integration with existing MATLAB workflows and customization of analysis parameters.