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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.
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