[robotpepi]

> So there's nothing about this particular sequence?

Kolakoski's sequence is conjectured to be "uniformly recurrent", which means that every block of contiguous symbols appearing once in the sequence appears infinitely often and with bounded gaps. This is clearly not true for any sequence constructed like this. And the fact that we don't know how to prove uniform recurrence for Kolakoski's, which is arguably the simplest sequence defined by this method, is remarkable. There are other conjectures about frequencies of symbols, etc.