Box-counting Dimension Method for Calculating Fractal Dimension of Curves

A MATLAB program developed using the box-counting dimension method can be employed to calculate the fractal dimension of curves. This method was originally introduced by mathematician Richard F. Voss in 1985 and has proven effective for analyzing and characterizing various complex natural and artificial structures, including cloud formations, tree branching patterns, river pathways, and more. The implementation typically involves covering the curve with boxes of different sizes and counting how the number of boxes needed changes with scale - the slope of the log-log plot of box count versus box size gives the fractal dimension. This program helps researchers better understand the shapes and characteristics of these structures, holding significant importance for both scientific research and engineering design. The MATLAB implementation usually includes functions for image preprocessing, box-size selection algorithm, and linear regression calculation for dimension estimation. Additionally, the box-counting dimension method finds applications in multiple fields such as image processing (for texture analysis and pattern recognition) and signal processing (for complexity assessment of time-series data), demonstrating broad application prospects. The code typically handles curve discretization, employs efficient counting algorithms using matrix operations, and includes visualization components for result validation.