Even in the absence of external stimuli, neural activity is both highly dynamic and organized across multiple spatiotemporal scales. The continuous evolution of brain activity patterns during rest is believed to help maintain a rich repertoire of possible functional configurations that relate to typical and atypical cognitive phenomena. Whether these transitions or “explorations” follow some underlying arrangement or instead lack a predictable ordered plan remains to be determined. Here, using a precision dynamics approach, we aimed at revealing the rules that govern transitions in brain activity at rest at the single participant level. We hypothesized that by revealing and characterizing the overall landscape of whole brain configurations (or states) we could interpret the rules (if any) that govern transitions in brain activity at rest. To generate the landscape of whole-brain configurations we used Topological Data Analysis based Mapper approach. Across all participants, we consistently observed a rich topographic landscape in which the transition of activity from one state to the next involved a central hub-like “transition state.” The hub topography was characterized as a shared attractor-like basin where all canonical resting-state networks were represented equally. The surrounding periphery of the landscape had distinct network configurations. The intermediate transition state and traversal through it via a topographic gradient seemed to provide the underlying structure for the continuous evolution of brain activity patterns at rest. In addition, differences in the landscape architecture were more consistent within than between subjects, providing evidence of idiosyncratic dynamics and potential utility in precision medicine.