"turned back on itself" is correct and usable in written English.
It is a phrase that describes something in a physical sense, usually when referring to something folding or wrapping around itself. For example: "The snake slithered around its prey and then suddenly turned back on itself, coiling its body into a tight circle."
Adding to speculation, Malaysian military radar indicates the missing plane turned back on itself shortly before vanishing.
The story of Metta World Peace, at least at this point in its arc, has turned back on itself.
The change in direction initially came on 9 March, when the Malaysian military announced that radar indicated that the plane turned back on itself shortly before vanishing, meaning it began travelling away from Beijing before disappearing.
The timber hitch, in which the rope is turned back on itself at least three times, is a rapidly tied variation that is used by loggers on tree trunks.
Walking that spiraling path, which turned back on itself several times — and turned me 180 degrees — before setting off in another direction, seems to switch the tracks in the brain.
The subtitle of the collection, as the editor explains, adapts a well-known saying of Firth's, which characterises linguistics as language turned back on itself, and very fittingly describes the general spirit of this volume.
In "Summer," particularly, it tends to wander, then to turn back on itself.
Imagine that sinuous and haunting melody, which keeps turning back on itself, burrowing ever deeper into your psyche.
Three Women is altogether more mysterious, turning inward, turning back on itself, allowing its characters to exchange or alter their basic natures.
This work, too, begins from basics in each of its five movements, sparking an organic growth that ultimately turns back on itself.
At the far end, after manifold adventures, the material turns back on itself, coming home to a hard-won calm, steeped in recollection.
