It's full of energy, symbolism and fun. However it's also a bit opaque, with an Alice in Wonderland plot that ends up going to some offbeat psychological places that may or may not involve coming-of-age, mother-daughter issues, reality warping, lesbians and/or a complete abandonment of free will. It was quite interesting, but to be honest I don't see myself particularly needing to rewatch it.
Cocona is clever, but a bit indecisive and definitely not looking for adventure. Papika, on the other hand, is like a puppy, being enthusiastic all over the place and charging immediately into any situation. She's hectic. Together they'll be the Flip-Flappers, visiting a new Pure Illusion universe every week and looking for crystal fragments of the Amorphous! It'll be amazing! They'll go to a desert island, a horror movie mansion and a fantasy acid trip dimension! They'll get caught in time loops with creepy dolls! They'll turn into animals! They'll visit a Mad Max desert world! They'll befriend an approximately rabbit-shaped green blob and keep it in a cage!
Well, that's Papika's plan anyway. Cocona doesn't like any of that and might even get hostile if she thinks she's being threatened with danger, unpredictability and getting in touch with herself. She's a nice girl, but she prefers to avoid taking risks and making choices. Cocona likes control. Papika thinks control is a thing for playing computer games.
The show's first half is full of one-off "Pocket Dimension Of The Week" episodes. There doesn't seem to be much plot, but there's lots of development of the Papika-Cocona relationship. Cocona in particular is the show's focus. She's the one who needs to grow. (Papika doesn't really do growth. To develop as a person, she'd have to slow down and think.) There are antagonists, after a fashion, but I wouldn't really call them villains and again I think the point of their presence in the series is more to explore their relationships with Cocona. All these episodes can get surreal, either in the ways you'd expect or by telling quiet and potentially baffling stories that are all about telling your name to someone's granny.
This isn't a plot-driven show, instead appearing to have two main goals:
1. playing with its characters, in ways that will get increasingly weird.
2. trying to put as much wild, cool and exciting stuff on screen as possible. This show is spectacularly animated. It's not tight and subtle, like Kyoto Animation, but instead loose and imaginative, like Studio Trigger. This is taken to the next level by the show's lack of interest in consistent consensus reality, instead being more about having a bugnuts story structure and looking for ways to surprise your eyeballs.
After a while, though, stuff starts happening. People get jealous and we meet someone impossible. Ep.11 has guns and the word "kill". Something happens with Cocona that you could analyse and look for meanings until your head exploded. We also have three or four characters who look the same, which is sometimes deliberate (one family resemblance and a ghost/duplicate/something SPOILER) and perhaps sometimes not (I was wondering whether or not Sayuri was meant to be SPOILER). There's more than one time zone, to go with the bubble universes. This isn't actually as confusing as you might think, since the real story is clearly the inner journey of Cocona and the other characters, but it's still a pretty rich soup. I'd have liked a bit more time spent explaining the significance of the organisations, for instance, both the Flip Flap organisation and their rivals, Asclepius, with the Amorphous Children. (This could be either literal, e.g. where they come from, or metaphorical, e.g. how they fit into the show's themes and symbolism.)
This show's weird and hard to describe. Its first half looks like an LSD trip. I could imagine dropping it because it seemed like a kiddie show, especially since the girls are only in junior high and Papika in particular acts younger than her age. They have a cartoon animal buddy (even if he is named after the Baltic German biologist who invented umwelt) and magical girl transformation sequences. However the second half unfolds in ways that might make this sound like two unrelated series bolted together if you try describing it to someone. It isn't. It feels more coherent than that. However it's an exercise in bending reality, time and plotting into whatever the animators though might be a laugh at the time, while throwing obscure highbrow references into what looks like lowbrow silly goofiness. Its storyline is almost entirely the inner journey of Cocona and others, with entire universes being used for metaphor. I could imagine two fans discussing it and not even realising they're talking about the same show. ("I still haven't finished unpacking the themes underneath the relationships." "It's a sugar rush for children and I dropped it after episode two.")
On reflection, that might be my favourite thing about it.