Cosmology in one dimension: Symmetry role in dynamics, mass oriented approaches to fractal analysis

The distribution of visible matter in the universe, such as galaxies and galaxy clusters, has its origin in the week uctuations of density that existed at the epoch of recombination. The hierarchical distribution of the universe, with its galaxies, clusters and super-clusters of galaxies indicates the absence of a natural length scale. In the Newtonian formulation, numerical simulations of a one-dimensional system permit us to precisely follow the evolution of an ensemble of particles starting with an initial perturbation in the Hubble ow. The limitation of the investigation to