  We investigate a phenomenon observed by W. Thurston wherein one constructs a
pseudo-Anosov homeomorphism on the limit set of a certain lift of a
piecewise-linear expanding interval map. We reconcile this construction with a
special subclass of generalized pseudo-Anosovs, first defined by de Carvalho.
From there we classify the circumstances under which this construction produces
a pseudo-Anosov. As an application, we produce for each $g \geq 1$ a
pseudo-Anosov $\phi_g$ on the surface of genus $g$ that preserves an
algebraically primitive translation structure and whose dilatation $\lambda_g$
is a Salem number.
