The aim of this paper is to study the closure of the orbit of sequence
s obtained by iterating maps on words g(u) = u.u1, d(u) = u.1[u.], and
product g . d, where u1 is word u without its last letter, 1u is word
u without its first letter and u. is its mirror image. It is shown th
at d thus generates a periodic orbit, g a subshift of finite type and
g . d an automatic sequence.