Similar universal phenomena can emerge in different complex systems when those systems share a common symmetry in their governing laws. In physical systems operating near a critical phase transition, the governing physical laws obey a fractal symmetry; they are the same whether considered at fine or coarse scales. This scale-change symmetry is responsible for universal critical phenomena found across diverse systems. Experiments suggest that the cerebral cortex can also operate near a critical phase transition. Thus we hypothesize that the laws governing cortical dynamics may obey scale-change symmetry. Here we develop a practical approach to test this hypothesis. We confirm, using two different computational models, that neural dynamical laws exhibit scale-change symmetry near a dynamical phase transition. Moreover, we show that as a mouse awakens from anesthesia, scale-change symmetry emerges. Scale-change symmetry of the rules governing cortical dynamics may explain observations of similar critical phenomena across diverse neural systems.