Figure reports the transitions detected for the ε = 45 kJ mol -1 system (see SI for data on the other systems and additional details). Two zoomed regions of the transition probability matrix are reported in Figure (left and right panels), identifying respectively the dynamics of smaller or larger aggregates. As summarized in the scheme of Figure , the off-diagonal pathways on the right (red arrow) signal polymerisation events, while the left ones (blue arrow) signal depolymerisation events. Noteworthy, at the equilibrium, small assemblies are more likely to aggregate into larger assemblies, rather than to disassemble -the probabilities are larger on the right-side of the diagonal (Figure , left). This is the case up to assemblies of size ∼ 33 -64 monomers for the ε = 45 kJ mol -1 system (but which depends on the ε value). As the range increases, the fibres become inherently less stable, and fragmentation becomes more likely than growth (Figures and). The tendency to self-assembly is thus contrasted by the increasing probability of fragmentation. These competing factors determine the dynamic equilibrium in the monomer exchange. When ε is decreased (40, kJ mol -1 ), the equilibrium shifts to smaller aggregate sizes (Figure : highest probability for ∼ 5 -16 monomers). Vice versa, for stronger monomer-monomer interactions (ε = 50, kJ mol -1 ) the equilibrium moves towards longer fibres (Figure : highest probability for ∼ 65 -128). We refer to (logarithmic) ranges of fibre sizes, as we aimed at a qualitative picture of how the equilibrium dynamics shapes the entities that are most probably observed (exact length values are less meaningful in such fluctuating complex systems).