Eternal Recurrence and Heraclitus

In his comments about Birth of Tragedy, appearing in Ecce Homo, Nietzsche suggests that Heraclitus could have preceded him in espousing a doctrine of Eternal Recurrence. At first glance, the attribution to a Philosopher best known for asserting that 'One never steps in the same river twice', a subscription to a doctrince of even a single Recurrence, seems extraordinary. However, Nietzsche's only sustained discussion of Heraclitus, included in his Philosophy in the Tragic Era of the Greeks, does offer a few clues that might explain the suggestion. First, he finds in Heraclitus both an exoteric and an esoteric version of a theory of Becoming--the ephemerality of existence proposed by the former obscures a regularity that is deciphered by the latter. Second, that regularity is an endless play of creation and destruction. Third, that play is constituted by a rhythm of monistic substance, i. e. Fire, diversifying itself and reconciling with itself. Accordingly, perhaps Nietzsche is himself hinting at an esoteric reading of the doctrine of Eternal Recurrence, e. g. that it is not so much the course of events that recurs, but its internal rhythm of creation and destruction, that, at bottom, is the play of Dionysus self-disintegrating and re-integrating.