  We consider Hamilton cycles in the random digraph $D_{n,m}$ where the
orientation of edges follows a pattern other than the trivial orientation in
which the edges are oriented in the same direction as we traverse the cycle. We
show that if the orientation forms a periodic pattern, other than the trivial
pattern, then approximately half the usual $n\log n$ edges are needed to
guarantee the existence of such Hamilton cycles a.a.s.
