Complexity and Persistence of Electrical Brain Activity Estimated by Higuchi Fractal Dimension

Brain electrical activity, as recorded through electroencephalography (EEG), displays scale-free temporal fluctuations indicative of fractal behavior and complex dynamics. This study explores the use of the Higuchi Fractal Dimension (HFD) as a proxy of two complementary aspects of EEG temporal organization: local signal irregularity, interpreted within a Kolmogorov-type framework, and persistence related to temporal structure, associated with statistical complexity. The latter can be used to evidence persistence in the EEG signal, serving as an alternative to previously used approaches for estimating the Hurst exponent. Thirty-eight healthy participants underwent resting-state EEG recordings in open- and closed-eyes conditions. HFD was computed for the original signals to assess Kolmogorov complexity and for the signals’ cumulative envelopes to evaluate statistical complexity and, consequently, persistence. The results confirmed that HFD values align with theoretical expectations: higher for random noise in the Kolmogorov model (~2) and lower in the statistical model (~1.5). EEG data showed condition-dependent and topographically specific variations in HFD, with parieto-occipital regions exhibiting greater complexity and persistence. The HFD values in the statistical model fall within the 1–1.5 range, indicating long-term correlation. These findings support HFD as a reliable tool for assessing both the local roughness and global temporal structure of brain activity, with implications for physiological modeling and clinical applications.