Left panel: measure of the two-point correlation dimension of the regular interactions of the sixth zoom-in level. The ordinate C(l) is the number of pairs with phase-space distance less than scale l. The grey dots includes all the realizations in the simulations, whose power-law fit (grey line) is close to its expected dimension (D ≃ 2). The orange dots only consider the regular set (f_col > 2/3), and its fractal dimension is lower than 2. Right panel: fractal dimension for each zoom level, as measured from the 2-point correlation dimension. The error bars represent the least-squared fit. The results for the 14th zoom-in are repeated using an arbitrary precision integrator, see Sec. 5.