Box-Counting Fractal Dimension Calculation for 1D Signals

The calculation of box-counting fractal dimension for one-dimensional signals is implemented using MATLAB. The box-counting fractal dimension method serves as a quantitative approach to characterize signal complexity. This algorithm operates by partitioning the signal into boxes of varying sizes and computing the fractal dimension within each box to quantify the signal's intricacy level. MATLAB provides a robust mathematical environment for signal processing and analysis, including specialized implementations for fractal dimension calculations. The typical implementation involves defining box sizes through logarithmic scaling, counting occupied boxes using threshold-based detection, and performing linear regression on the log-log plot of box counts versus box sizes to extract the fractal dimension. Key MATLAB functions often utilized include array manipulation tools for signal segmentation, logical indexing for box occupancy determination, and polyfit for dimension estimation from the slope of the regression line.