Preissl H, Lutzenberger W, Pulvermüller F, Birbaumer N
Institut für Medizinische Psychologie und Verhaltensneurobiologie, Universität Tübingen, Germany.
Neurosci Lett. 1997 Apr 4;225(2):77-80. doi: 10.1016/s0304-3940(97)00192-4.
Fractal dimensions has been proposed as a useful measure for the characterisation of electrophysiological time series. But one of the problems of this approach, is the difficulty to record time series long enough of determine the 'real' fractal dimension. Nevertheless it is possible to calculate fractal dimensions for very short data-segments. Using time series of different length it is possible to show, that there is a monotoneous relation between fractal dimension and the number of data-points. This relation could be further interpreted with the help of an extrapolation scheme. In addition this effect is also seen with surrogate data, generated from that signal. We conclude that it is feasible to use fractal dimension as a tool to characterise the complexity for short electroencephalographic (EEG) time series, but it is not possible to decide whether the brain is a chaotic system or not.
分形维数已被提议作为表征电生理时间序列的一种有用度量。但这种方法的问题之一是难以记录足够长的时间序列来确定“真实”的分形维数。然而，对于非常短的数据段计算分形维数是可能的。使用不同长度的时间序列可以表明，分形维数与数据点数量之间存在单调关系。借助外推方案可以进一步解释这种关系。此外，从该信号生成的替代数据也能看到这种效应。我们得出结论，使用分形维数作为表征短脑电图（EEG）时间序列复杂性的工具是可行的，但无法确定大脑是否为混沌系统。
