The World of Ice
Himari has a strange dream in which she meets a man named Sanetoshi, who shows her various books containing her memories. In elementary school, she formed a group called Triple-H with her best friends, Hibari and Hikari. When she argued with her mother over buying a wrong ribbon, her mother became scarred from a falling mirror, she and her friends tried to kill a koi for its blood to heal her mother. She left elementary school due to her illness whilst her friends went on to become idols. Upon waking up after vaguely recollecting a soulmate she once had, Himari hears from Ringo about Shoma's accident.
Aired 09/09/2011EP 9 - The World of Ice

Penguindrum
Once you make a decision, does the universe conspire to make it happen? Is destiny a matter of chance, a matter of choice or the complex outcome of thousands of warring strands of fate? All twins Kanba and Shoma know is that when their terminally ill sister Himari collapses at the aquarium, her death is somehow temporarily reversed by the penguin hat that she had asked for. It's a provisional resurrection, however, and it comes at a price: to keep Himari alive they need to find the mysterious Penguin Drum. In order to do that, they must first find the links to a complex interlocking chain of riddles that has wrapped around their entire existence, and unravel the knots that tie them to mystifying diary and a baffling string of strangers and semi-acquaintances who all have their own secrets, agendas and "survival strategies." And in order for Himari to live, someone else's chosen destiny will have to change. It's a story of love, fate, life, death... and Penguins!
(Source: Sentai Filmworks)