MATLAB Box-Counting Dimension Fractal Analysis

This document presents a highly practical fractal computation program implemented in MATLAB, suitable for applications in stock market analysis, materials science, medical research, and rock physics. The program utilizes MATLAB's advanced mathematical computing environment, which is widely adopted in scientific and engineering disciplines. The core algorithm implements the box-counting dimension method, which calculates fractal dimensions by systematically partitioning data space into increasingly smaller boxes and counting the occupied boxes at each scale. This approach enables researchers to quantitatively analyze complex patterns and irregular structures through key functions like grid generation, occupancy detection, and logarithmic regression analysis. Through this fractal computation program, users can effectively analyze stock market volatility trends, investigate microscopic material structures, assist in disease diagnosis and treatment, and characterize rock physical properties. The program's modular architecture provides flexibility and extensibility, allowing customization through parameter adjustments in functions such as 'calc_fractal_dimension' and 'box_count' for specific research requirements. With its comprehensive set of algorithms including data preprocessing, dimension calculation, and visualization tools, this solution serves as a preferred tool for professionals across multiple domains, demonstrating significant application potential in both academic research and industrial practice.