Recent findings identified electroencephalography (EEG) microstates as the electrophysiological correlates of fMRI resting-state networks. Microstates are defined as short periods (100 ms) during which the EEG scalp topography remains quasi-stable; that is, the global topography is fixed but strength might vary and polarity invert. Microstates represent the subsecond coherent activation within global functional brain networks. Surprisingly, these rapidly changing EEG microstates correlate significantly with activity in fMRI resting-state networks after convolution with the hemodynamic response function that constitutes a strong temporal smoothing filter. We postulate here that microstate sequences should reveal scale-free, self-similar dynamics to explain this remarkable effect and thus that microstate time series show dependencies over long time ranges. To that aim, we deploy wavelet-based fractal analysis that allows determining scale-free behavior. We find strong statistical evidence that microstate sequences are scale free over six dyadic scales covering the 256-ms to 16-s range. The degree of long-range dependency is maintained when shuffling the local microstate labels but becomes indistinguishable from white noise when equalizing microstate durations, which indicates that temporal dynamics are their key characteristic. These results advance the understanding of temporal dynamics of brain-scale neuronal network models such as the global workspace model. Whereas microstates can be considered the "atoms of thoughts," the shortest constituting elements of cognition, they carry a dynamic signature that is reminiscent at characteristic timescales up to multiple seconds. The scale-free dynamics of the microstates might be the basis for the rapid reorganization and adaptation of the functional networks of the brain.