Radial density profile measured at various times in the VlaSolve simulations, namely initial conditions (blue dashes), intermediate time used to perform tests of self-similarity of the phase-space spiral (green), and final time (red dashes). For the final time, the results are also compared to a Gadget-2 run (thick grey), as well as the output of the shell code (thick grey dashes) for (η, n) = (0.1, −1) and (0.1, −1.5). In addition, the logarithmic slopes −4 and −2.1 (as measured in Hozumi et al. 2000) are shown respectively as a thin solid and a thin dashed line.