Box Counting Algorithm for Fractal Dimension Calculation

In the following section, I present the source code for calculating fractal dimensions using the box counting algorithm. This implementation is written in MATLAB and includes comprehensive code annotations to facilitate understanding for researchers and students interested in fractal theory. The box counting algorithm is a fundamental method for estimating fractal dimensions by systematically covering a shape with progressively smaller boxes and counting how many boxes contain parts of the shape. This technique finds applications in various fields including digital image processing, geographical information systems (GIS), and complex pattern analysis. My MATLAB implementation demonstrates the practical application of the box counting algorithm through these key components: - Grid partitioning functionality that recursively divides the spatial domain into smaller boxes - Binary image processing capabilities for shape analysis - Logarithmic scaling calculations for dimension estimation using the formula: D = lim(ε→0) [log N(ε) / log(1/ε)] - Visualization routines to plot the log-log graph of box size versus box count The code includes detailed comments explaining each computational step, making it accessible for MATLAB users at different proficiency levels. This implementation aims to provide both a practical tool for fractal dimension calculation and an educational resource for understanding the underlying mathematical concepts.