  We write a non-relativistic Lagrangian for a hierarchical universe. The
equations of motion are solved numerically and the evolution of the fractal
dimension is obtained for different initial conditions. We show that our model
is homogeneous at the time of the last scattering, but evolves into a
self-similar universe with a remarkably constant fractal dimension. We also
show that the Hubble law is implied by this model and make an estimate for the
age of the universe.
