A dynamical approach to a self-similar universe

We write a non-relativistic Lagrangian for a hierarchical universe. The equ ations of motion are solved numerically and the evolution of the fractal di mension is obtained for different initial conditions. We show that our mode l is homogeneous at the time of the last scattering, but evolves into a sel f-similar universe with a remarkably constant fractal dimension. We also sh ow that the Hubble law is implied by this model and make an estimate for th e age of the universe.