This is an analysis of the kinematics of 20 cosmological voids using an oscillator model. Two scaling laws have been discovered: (1) the amplitude of the oscillations is proportional to the radius of the void ($A \ approximately 0.1 R$), and (2) the oscillation period is scaled as $T \propto R^{0.35}$. These laws point to scale-invariant fractal dynamics in the large-scale evolution of structures, providing a new quantitative basis for the study of voids.