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The whole idea of convergence is an interesting one. We can see it in physics, and by extension, in biology. E.g. there are marsupial "wolves" in the fossil record that require expertise to differentiate from placental wolves, because the two creatures converged to such a high degree. These convergences are a result of creatures "solving" physical problems in their environment. So physics dictates biologic form in many cases.
Have you come across D'Arcy Thompson? He spent great effort in his career trying to generalize convergent trends in evolution based on simple mathematical models (well, as simple as he could make them). He was writing before information theory was discovered. I suspect that if physical laws are generalize-able from information theory that evolutionary trends must be, as well, given that species are forged as one possibility among seemingly infinite states. (Interestingly, I first came across Kolmogorov when studying mathematical biology; there's a strange convergence!)
I promised myself I'll work today so this (and you too mk) will have to wait until the p.m. as this is a very deep and interesting discussion that deserves attention.
(Yes. I love On Growth and Form. [arch school days and my obsession to create a morphological system for generating buildings. Remember that drawing?])