Tous les systèmes hamiltoniens intégrables se ressemblent, mais chacun qui est non intégrable, il est non intégrable à sa manière
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The vfplot program plots arrows up to the boundary, treating that boundary as a wall against which the arrows should be packed carefully. But for some vector fields the boundary is just a selection from a larger theoretical model, possibly infinite or semi-infinite. This extent "beyond the plot" can be indicated visually by cropping the plot on one-or-more sides.
The Boussinesq flow plot crops just the top and bottom of the field, indicating and pipe which is vertically unbounded.