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 \(\mu < {\mu }_{{\rm{split}}}\simeq 14\) but in panel (c) with \(N=250\) it occurs for \(\mu < {\mu }_{{\rm{split}}}\simeq 22\), providing evidence that the critical value for splitting increases with system size.