Non-standard fractal spectrum of a 1D gravitating model

A one-dimensional (1D) system obeying the Hubble expansion is studied numerically using an N-body code. The rescaling of both space and time changes the dynamics which, in the rescaled frame, is analogous to the dynamics of a 1D one-component plasma with the addition of a friction term. We start from a homogeneous initial condition but, because of Jeans’ instability, the system enters a non-linear regime and builds a hierarchical structure. Applying a multi-fractal analysis, we show that the density reveals a non-standard fractal spectrum related to a bifractal geometry.