BACKGROUND: Neurosurgical management of brain tumors has entered a paradigm of supramarginal resections that demands thorough understanding of peritumoral functional effects. Historically, the effects of tumors have been believed to be local, and long-range effects have not been considered. OBJECTIVE: To test the hypothesis that tumors affect the brain globally, producing long-range gradients in cortical function. METHODS: Resting-state functional magnetic resonance imaging (fMRI) data were acquired from 11 participants with glioblastoma and split into discovery and validation datasets in a single-center prospective cohort study. Fractal complexity was computed with a wavelet-based estimator of the Hurst exponent. Distance-related effects of the tumors were tested with a tumor mask-dilation technique and parcellation of the underlying Hurst maps. RESULTS: Fractal complexity demonstrates a penumbra of suppression in the peritumoral region. At a global level, as distance from the tumor increases, this initial suppression is balanced by a subsequent overactivity before finally normalizing. These effects were best fit by a quadratic model and were consistent across different network construction pipelines. The Hurst exponent was correlated with graph theory measures of centrality including network robustness, but graph theory measures did not demonstrate distance-dependent effects. CONCLUSION: This work provides evidence supporting the theory that focal brain tumors produce long-range gradients in function. Consequently, the effects of focal lesions need to be interpreted in terms of the global changes on functional complexity and network architecture rather than purely in terms of functional localization. Determining whether peritumoral changes represent potential plasticity may facilitate extended resection of tumors without functional cost.