Snapshots of a Monte Carlo experiment computed for λ = 0.204 and Titan’s nominal migration rate. This experiment features 101 values of initial obliquity between 0° and 60°, for which 240 values of initial precession angle are regularly sampled in [0, 2π). The value of α reached by the trajectories at the time of the snapshot is labelled on each panel. Each trajectory is represented by a small dot which is coloured according to the variation range of the resonant angle σ₃ (obtained bya 0.5-Gyr numerical integration with constant α). The horizontal green line shows the current obliquity of Saturn. At the beginning of the propagations, all trajectories are coloured red (since σ₃ circulates), and distributed along a diagonal line. Then, as α increases over time, trajectories are dispersed off the diagonal according to the four types of trajectories depicted in Fig. 4 and labelled in the penultimate panel.