  Recently the area of tropical geometry has introduced the concept of the
tropical elliptic group law associated with a tropical elliptic curve. This
gives rise to a notion of the tropical QRT mapping. We compute the explicit
tropically birational expressions that define the tropical QRT mapping for some
arbitrary set of parameters. We consider this a new integrable ultradiscrete
system. This also induces a new notion of tropical elliptic functions,
different to the ultradiscretized elliptic functions.
