MATLAB Code for Fractal Dimension Calculation in Time Series Analysis

This MATLAB code provides specialized implementation for calculating fractal dimension in time series data. Fractal dimension serves as a crucial mathematical metric for quantifying pattern complexity and irregularity in temporal data sequences. The implementation supports analysis of diverse phenomena including financial market fluctuations, natural environmental patterns, and medical signal processing. The code employs established fractal dimension computation algorithms such as box-counting method or Higuchi's method, which systematically analyze the self-similarity properties and scaling characteristics of time series data. Key functions include data preprocessing for noise reduction, multi-scale analysis implementation, and dimension calculation routines that output standardized fractal dimension metrics. After computing the fractal dimension values, users can leverage these quantitative measures for advanced analytical applications including complexity assessment, pattern recognition, and predictive modeling of future trends. The implementation features configurable parameters for algorithm selection, scale range specification, and precision control to accommodate various research requirements. This toolbox serves as an essential resource for researchers and analysts working with temporal data complexity, providing robust mathematical foundations for understanding intricate patterns in time-dependent phenomena through validated fractal geometry principles.