The Brain in Fractal Time: 1/F-Like Power Spectrum Scaling of the Human Electroencephalogram

"1/f-like" power spectrum scaling is a ubiquitous feature of complex systems. In such scaling, the power spectrum of a given time series is dominated by an inverse power law, resulting in an inverse linear relation between log power and log frequency. The 1/f-like power spectrum scaling properties of human, resting eyes-closed and eyes-open EEG were examined. For both eyes-closed and eyes-open EEG, log power had a significant inverse linear relation with log frequency. The slope of this relation was not correlated with previously-calculated Grassberger-Procaccia dimension estimates for the same data, indicating that the EEG is not a 1/f-like stochastic process. Further, the degree of deviation from perfect log power versus log frequency linearity was related to power in the 8-12 Hz alpha frequency band. It is speculated that this deviation may be related to the low dimension of a chaotic alpha rhythm relative to other EEG rhythms.