  An infinite family of generalized pseudo-Anosov homeomorphisms of the sphere
S is constructed, and their invariant foliations and singular orbits are
described explicitly by means of generalized train tracks. The complex strucure
induced by the invariant foliations is described, and is shown to make S into a
complex sphere. The generalized pseudo-Anosovs thus become quasiconformal
automorphisms of the Riemann sphere, providing a complexification of the
unimodal family which differs from that of the Fatou/Julia theory.
