  Devaney and Krych showed that for the exponential family $\lambda e^z$, where
$0<\lambda <1/e$, the Julia set consists of uncountably many pairwise disjoint
simple curves tending to $\infty$. Viana proved that these curves are smooth.
In this article we consider a quasiregular counterpart of the exponential map,
the so-called Zorich maps, and generalize Viana's result to these maps.
