Computing Fractal Box Dimension for One-Dimensional Signals or Functions

Compute the fractal box dimension for one-dimensional signals or functions. The fractal box dimension is a mathematical concept used to measure the complexity of fractal objects. This dimension is calculated by dividing the object into a series of boxes and determining the minimum number of boxes required to cover it entirely. The algorithm implementation typically involves iterating through different box sizes (e.g., using powers of 2 for computational efficiency) and counting the non-empty boxes containing signal data points. Key functions would include box-counting routines with logarithmic scaling for dimension estimation. Fractal box dimension helps understand the self-similarity and scale invariance properties of one-dimensional signals or functions, revealing their intrinsic structures and characteristics. Through computation of fractal box dimension, we can conduct deeper research and analysis of signal properties, with applications across various fields including physics (for analyzing chaotic systems), engineering (for signal processing and noise characterization), and biology (for EEG signal analysis and physiological pattern recognition). Code implementation often involves preprocessing signals, handling edge cases, and using linear regression on log-log plots to extract the dimension value from the slope.