MATLAB Source Code for Calculating Generalized Fractal Dimensions

This MATLAB source code provides a comprehensive implementation for calculating generalized fractal dimensions. For researchers conducting fractal analysis on data sets, this serves as a valuable computational tool. The program enables calculation of fractal dimensions across different q-values, where q=0 corresponds to Hausdorff dimension, q=1 to Information dimension, and q=2 to Correlation dimension, among others. The core functionality is implemented through the function [dq, rq] = fdim(q, x, trace), where 'q' represents the order parameter, 'x' is the input data vector, and 'trace' controls verbose output. The algorithm processes data through multiple scaling regions using box-counting techniques, performing linear regression on log-log plots to extract dimension estimates. Users can obtain fractal dimensions for various q-values and perform subsequent analysis as needed. The code includes adjustable parameters for precision control and scaling range selection. For detailed implementation specifics and parameter explanations, please refer to the comprehensive comments within the source code.