Fractals and the analysis of waveforms

摘要: Waveforms are planar curves--ordered collections of (x, y) point pairs--where the x values increase monotonically. One technique for numerically classifying waveforms assesses their fractal dimensionality, D. For waveforms: D = log(n)/(log(n) + log(d/L], with n number steps in waveform (one less than pairs), d extent (diameter) waveform, and L total length waveform. Under this formulation, dimensions range from 1.0, straight lines through approximately 1.15 random-walk waveforms, to approaching 1.5 most convoluted waveforms. The characterization may be especially useful analyzing comparing complex such as electroencephalograms (EEGs).