  The $\mathbf{g}$-vector fan of a finite-dimensional algebra is a fan whose
rays are the $\mathbf{g}$-vectors of its $2$-term presilting objects. We prove
that the $\mathbf{g}$-vector fan of a tame algebra is dense. We then apply this
result to obtain a near classification of quivers for which the closure of the
cluster $\mathbf{g}$-vector fan is dense or is a half-space, using the additive
categorification of cluster algebras by means of Jacobian algebras. As another
application, we prove that for quivers with potentials arising from
once-punctured closed surfaces, the stability and cluster scattering diagrams
only differ by wall-crossing functions on the walls contained in a separating
hyperplane. The appendix is devoted to the construction of truncated twist
functors and their adjoints.
