  We study a one dimensional model of gravitational instability in an
Einstein-de Sitter universe. Scaling in both space and time results in an
autonomous set of coupled Poisson-Vlasov equations for the field and phase
space density, and the $N$-body problem. Using dynamical simulation, we find
direct evidence of hierarchical clustering. A multi-fractal analysis reveals a
bifractal geometry similar to that observed in the distribution of galaxies. To
demonstrate the role of scaling, we compare the system to other one dimensional
models recently employed to study structure formation. Finally we show that the
model yields an estimate of the time of galaxy formation of the correct order.
