The brain shows a topographical hierarchy along the lines of lower- and higher-order networks. The exact temporal dynamics characterization of this lower-higher-order topography at rest and its impact on task states remains unclear, though. Using 2 functional magnetic resonance imaging data sets, we investigate lower- and higher-order networks in terms of the signal compressibility, operationalized by Lempel–Ziv complexity (LZC). As we assume that this degree of complexity is related to the slow–fast frequency balance, we also compute the median frequency (MF), an estimation of frequency distribution. We demonstrate (i) topographical differences at rest between higher- and lower-order networks, showing lower LZC and MF in the former; (ii) task-related and task-specific changes in LZC and MF in both lower- and higher-order networks; (iii) hierarchical relationship between LZC and MF, as MF at rest correlates with LZC rest–task change along the lines of lower- and higher-order networks; and (iv) causal and nonlinear relation between LZC at rest and LZC during task, with MF at rest acting as mediator. Together, results show that the topographical hierarchy of lower- and higher-order networks converges with their temporal hierarchy, with these neural dynamics at rest shaping their range of complexity during task states in a nonlinear way.