Figure 11.

We plot in different panels the probability density function of the number of groups for fixed p but different μ for the initial condition $x_0=0.5$, ${\ell }_0=0.5$. The distributions with the same color in panel (a and b) correspond to the same μ but different p and are, roughly speaking, indistinguishable, implying that, for these particular initial conditions, the mean value and the variance of $f_{\#groups}$ do not depend on p but on μ. In addition we can see that in panels (a and b) with $N=30$ splitting occurs for $\mu <{\mu }_{\mathrm{split}}\simeq 14$ but in panel (c) with $N=250$ it occurs for $\mu <{\mu }_{\mathrm{split}}\simeq 22$, providing evidence that the critical value for splitting increases with system size.