Relating brain dynamics acting on time scales that differ by at least an order of magnitude is a fundamental issue in brain research. The same is true for the observation of stable dynamical structures in otherwise highly non-stationary signals. The present study addresses both problems by the analysis of simultaneous resting state EEG-fMRI recordings of 53 patients with epilepsy. Confirming previous findings, we observe a generic and temporally stable average correlation pattern in EEG recordings. We design a predictor for the General Linear Model describing fluctuations around the stationary EEG correlation pattern and detect resting state networks in fMRI data. The acquired statistical maps are contrasted to several surrogate tests and compared with maps derived by spatial Independent Component Analysis of the fMRI data. By means of the proposed EEG-predictor we observe core nodes of known fMRI resting state networks with high specificity in the default mode, the executive control and the salience network. Our results suggest that both, the stationary EEG pattern as well as resting state fMRI networks are different expressions of the same brain activity. This activity is interpreted as the dynamics on (or close to) a stable attractor in phase space that is necessary to maintain the brain in an efficient operational mode. We discuss that this interpretation is congruent with the theoretical framework of complex systems as well as with the brain’s energy balance.