@PrettyGnosticMaschine @licho
Heh, the funny thing is, that 'phase transition' is a really good term here. Even if it doesn't match the technical definition, which I wouldn't be too sure about, it pinpoints the concept really well.
Imagine that order parameter, and tune it from ordered (frozen, low energy, boring) to chaos (hot, crazy...) at some point certain systems will have a small regime where it is neither not, but rather complex. Many (complex) systems exhibit such behavior, such as the brain, internet connectivity and many other graphs. At this point they show funny properties, one of them is scale-invariance, i. e. the system looks the same at every 'zoom level'. Features appear over and over again, at any given size.
This is exactly the property of fractals!
I believe the brain is at this very edge, between boring and crazy, where self-referencing becomes possible, maybe even unavoidable, but that is too far of a stretch to make a real assertion while babbling here. Nevertheless I like how it circles around :)