All of the articles I have read thus far on self-organizing systems wrt abiogenesis have been unable to explain the rise of syntax and autonomy - even taking information as a cosmic "given" (source unknown).
Also, as you have mentioned - even with self-organizing systems (and cellular automata btw) - there are always "guides" to the system.
Order cannot rise spontaneously from an unguided physical system. Period.
Or maybe that should be "periodic"...
Just for kicks, have you looked up Liesengang rings?
Full Disclosure: I did a college P-chem project on them when I was a young kitten.
Cheers!