Dynamic power management (DPM) is critical to maximizing the performance of systems ranging from multicore processors to datacenters. However, one formidable challenge with DPM schemes is verifying that the DPM schemes are correct as the number of computational resources scales up. In this paper, we develop a DPM scheme such that it is scalably verifiable with fully automated formal tools. The key to the design is that the DPM scheme has fractal behavior; that is, it behaves the same at every scale. We show that the fractal design enables scalable formal verification and simulation shows that our scheme does not sacrifice much performance compared to an oracle DPM scheme that optimally allocates power to computational resources. We implement our scheme in a 2-socket 16-core x86 system and experimentally evaluate it. © 2014 IEEE.