Chäos;HEAd continues along its slightly confusing and messed up path exactly as you'd expect it to in episode three, even referencing dissociative identity disorder to add a little real-world bulk to this otherwise supernatural show.
After having Yua confront Takumi, suggesting that he is in some way responsible for the "New Gene" murders in the last episode, we first and foremost get a flashback to our protagonist's past - Namely, an occasion where his parents didn't allow him to go on a school field trip, and his resulting frustration and wishes seemingly turned into a real-life disaster, with the bus crashing and injuring/killing his classmates (it isn't made clear exactly what happened). Can Takumi really predict the future, and more importantly is he doing things he doesn't even remember in his sleep? Takumi visits a psychologist to find out if he's sleep-walking, but the results seem to suggest that isn't the case.
From here, further research on Takumi's part takes him to a gig by a band called Phantasm, and their lead singer Fes (a girl bearing more than a passing resemblance to a student at Takumi's school...), who seems to cross-reference important points that tie in with the New Gene killings in her band's lyrics. Takumi also starts seeing girls hanging around with huge swords, which appears to be another hint regarding what it to come in future episodes...
Once again, Chäos;HEAd delights in its refusal to separate any kind of real-world reality from what may or may not be Takumi's delusions, running it all together in a single storyline so that you really can't be entirely sure what's going on. The introduction of those big swords that only Takumi can see is probably the biggest hint yet as to where the series is going, although even that doesn't really give us a lot to work with, and aside from that (admittedly far from minor) point we really don't progress very far in terms of being educated as to what the Hell is going on - Mind you, this sense of mystery is actually working in favour of the series as far as I'm concerned. Takumi may remain hugely unlikeable as a person, but somehow this series continues to draw me into its web of intrigue on account of its rather unique story-telling perspective coupled with a solid enough plot to make the episodes fly by in an interesting and entertaining fashion. - Just the kind of thing to leave me wanting more.