  An irrational toric variety X is an analytic subset of the simplex associated
to a finite configuration of real vectors. The positive torus acts on X by
translation, and we consider limits of sequences of these translations. Our
main result identifies all possible Hausdorff limits of translations of X as
toric degenerations using elementary methods and the geometry of the secondary
fan of the vector configuration. This generalizes work of Garcia-Puente et al.,
who used algebraic geometry and work of Kapranov, Sturmfels, and Zelevinsky,
when the vectors were integral.
