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We exploited intracranial electroencephalogram data from 38 cortical regions using the Higuchi fractal dimension (HFD) as measure to assess brain complexity, on a dataset of 1772 electrode locations. HFD values depended on sleep stage and topography. HFD increased with higher levels of vigilance, being highest during wakefulness in the frontal lobe. HFD did not change from wake to stage N2 in temporo-occipital regions. The transverse temporal gyrus was the only area in which the HFD did not differ between any two vigilance stages. Interestingly, HFD of wakefulness and stage R were different mainly in the precentral gyrus, possibly reflecting motor inhibition in stage R. The fusiform and parahippocampal gyri were the only areas showing no difference between wakefulness and N2. Stages R and N2 were similar only for the postcentral gyrus. 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