Development of fractal geometry in a one-dimensional gravitational system

We study a one dimensional model of gravitational instability in a matter dominated universe. Careful scaling in both space and time results in an N-body problem governed by an autonomous set of coupled equations for the evolution of the system in phase space. Using dynamical simulation, we demonstrate that the system exhibits hierarchical structure formation. In common with galaxy observations, careful analysis suggests that, as time evolves, the distribution of particle positions develops bifractal geometry.