In a word, yes, because emergent properties are, by definition, not derivable by any means other than direct observation (which some might even argue is entirely subjective).
Put another way, the only way to detect any emergent mathematical pattern(s) of behavior from any complex system is to:
a) detect some isomorphic correspondence between what you want to find, and what is observed from the complex system as it evolves, then
b) calculate an error function capable of producing a metric for the difference between what you're looking for, and what is observed in the evolving complex system, then
c) if the error function is significant, tweak or replace the rules of the complex system, then go back to step (a).
If the above looks suspiciously like the scientific method, that's because it basically is. And just as ambiguous, as it turns out (if not more so), because there are (currently?) no guidelines, much less rules, for how to ""tweak" the rules of a complex system to better "fit" what you're looking for. Neither is there (currently?) any guidelines for how one might go about "detecting" emergent mathematical patterns in any given complex system (again, highly subjective, possibly very much so).
Alternatively, you might consider taking a hint from modern-day Cosmology / Fundamental Physics, and changing step (c) to:
c) if the error function is significant, announce to the world that you have discovered a new "particle" and call it "Dark ______" (fill in the blank), the properties of which are exactly defined by the aforementioned error function.
Regardless, implementation of the above could theoretically be accomplished by using the aforementioned "error function" as an inverse fitness function in a large-scale Evolutionary Computation.
Piece of cake, really, if you happen to have a couple of unused networked supercomputers lying around.. ;)