Scattering diagrams: polynomiality and the dense region

We use deformations and mutations of scattering diagrams to show that the coefficients of a scattering diagram with initial functions $f1=(1+tx{)}^{\mu }$ and $f2=(1+ty{)}^{\nu }$ are polynomial in $\mu$, $\nu$ and non-trivial in a certain dense region. We discuss consequences for Gromov-Witten invariants and quiver representations.