Fractale(2011)

Original title: フラクタル

Clain lives quietly amongst doppels—holograms that replace his parents and friends. Alone on a typical day, he saves a shrine maiden from pursuers and treats her wounds. He’s mystified by her worldly charms, but she disappears—leaving only a pendant behind. When a curious girl emerges from the amulet, Clain’s life takes a chaotic turn as he seeks to unlock the secrets his new friend holds.