(There are going to be massive spoilers here for Flip Flappers, and of course this is speculation.)

At this point it seems pretty clear that some or many settings (or worlds) in Pure Illusion are not arbitrary but instead come from something or someone (or maybe in some cases represent things). So here are my theories about the source of the main worlds from each episode so far, up through episode 8 (at the moment).

• episode 1: tentatively Cocona herself. The world is frozen over but the sun comes up when Cocona moves herself to action, and it feels a quite Cocona-thematic setting in retrospect (well, Cocona as she is at the start of Flip Flappers).

• episode 2: Uexküll and the insides of the school's roof cleaning system.

• episode 3: Unknown. An interesting speculation would be that it's Papika.
  Update: it's from Sayuri.
• episode 5: Unknown. If you want to attribute episode 3's setting to Papika, I'd turn around and attribute this one to Cocona, as then they make a thematic pair (and say some interesting things).

  Update: it's probably Yayaka.

• episode 6: Iroha Irodori, of course. Even the Pure Illusion world they're in before they enter what is either her past or her mind is made in the colours and style of her paintings.

• episode 7: I feel it's unknown, although you could argue that it's Cocona again. If it is Cocona, it means that two fragments/amorphous have been recovered from Cocona-based worlds (one from ep 1, by Cocona, and one here, by Yayaka's team). I'm willing to believe this, as Cocona is clearly something special.

• episode 8: TT-392, who we know has a human or at least biological brain inside its chassis (seen in episode 1 and a couple of times since).

My overall view is that not all Pure Illusion worlds are neatly tied into the cast, so I think that the PI worlds in 3 and 5 are not due to anyone or anything we've seen. As far as episode 7 goes, my theory is that the PI setting there was originally something else (and from someone else), but it was basically hijacked by Cocona falling into it with unresolved issues; her presence warped it into something that reflected her worries.

(This entry may get updated to add more episodes.)

Update:

• episode 9: likely Yayaka; all the signs seem to point that way.

Update: I wrote a part 2 about new information on episode 3 that was revealed in episode 11, a strong theory about episode 5 from Emily Rand, more argument about episode 9, and a general wrapup in which I conclude that we aren't going to find any more good evidence in the show.