An information stream contains a pattern if and only if
it can be compressed and reexpanded without loss,
otherwise it is random. (See Dennett's "Real Patterns"
in the Journal of Philosophy 1991, though he gets it
from someone else, whose details I don't recall right
now, but can get if required.)
I guess maybe what we're really arguing about is the
nature of information: does it exist "out there",
independently of us, or is it only in our minds. I go
along with the information theorists, physicists, etc,
and say it's out there, though, of course, the
argument is at least partly about definitions, as
seemingly always.
Robin