Fractals and the analysis of waveforms.
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 of steps in the waveform (one less than the number of (x, y) point pairs), d = planar extent (diameter) of the waveform, and L = total length of the waveform. Under this formulation, fractal dimensions range from D = 1.0, for straight lines through approximately D = 1.15 for random-walk waveforms, to D approaching 1.5 for the most convoluted waveforms. The fractal characterization may be especially useful for analyzing and comparing complex waveforms such as electroencephalograms (EEGs).
Katz
M J
MJ
Bio-architectonics Center, CWRU School of Medicine, Cleveland, OH 44106.
D005075:Biological Evolution; D004562:Electrocardiography; D004569:Electroencephalography; D008433:Mathematics; D010363:Pattern Recognition, Automated