Ranging fromRe=100toRe=20,000,severalcomputationalexperimentsare conducted, Rebeingthe Reynolds number. Theprimaryvortexstaysput, andthelongtermdynamic behaviorofthesmall vorticesdetermines thenatureof thesolutions. For lowReynolds numbers, thesolution isstationary; formoderateReynolds numbers, itis time periodic. For high Reynolds numbers, the solution is neither stationary nor time periodic: the solution becomes chaotic. Of the small vortices, the merging and the splitting, the appearance and the disappearance, and, sometime, the dragging away from one corner to another and the impeding of the merging—these mark the route to chaos. For high Reynolds numbers, over weak fundamental frequencies appears a very low frequency dominating the spectra—this very low frequency being weaker than clear-cut fundamental frequencies seems an indication that the global attractor has been attained. The global attractor seems reached for Reynolds numbers up to Re=15,000. This is the lid-driven square cavity ﬂow; the motivations for studying this ﬂow are recalled in the Introduction.