  In 1984 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 $\infty$, which they called hairs.
Viana proved that these hairs are smooth. Bara\'nski as well as Rottenfusser,
R\"uckert, Rempe and Schleicher gave analogues of the result of Devaney and
Krych for more general classes of functions. In contrast to Viana's result we
construct in this article an entire function, where the Julia set consists of
hairs, which are nowhere differentiable.
