Right . . . sorry about that. I don't pretend to completely understand the literature in this area, but to my knowledge, many of these complex processes (e.g. collective decision-making by ants, fish schools, bird flocks, etc.) are modeled such that random variables (drawn from a Normal distribution) are incorporated into the behavior of individuals in the groups. This is what I mean by stochastic - there's a random variable somewhere in the modeling process.

For example . . . an individual fish's directional preference might be a function of a bit of information it has about a resource patch somewhere, where it is with respect to other fish in its vicinity (it wants to stay with the group, but not get too close to other fish), the presence of predators, and then some random noise, which could be due to a combination of sensory error, tiny heterogeneities in the pressure on either side of the fish, etc. (that's the stochastic part . . . interestingly, these collective systems often don't work at all without the noise component incorporated).

When you put a bunch of 'fish' in a simulated 3-D environment with a few simple behavioral rules (as above), they can collectively choose the most efficient resource patches (even if only a few individuals have information), avoid predators, divide and re-fuse, and do all other sorts of incredible things. To my knowledge, this process has not and cannot be captured by conventional mathematics - perhaps it can be coarsely approximated, but not captured in full. That's how we justify using the word "emergence" in this context.

So, in one sense (which you have stressed), everything is determined, in that the future invariably depends on the exact current conditions of the universe. But in another sense, the behavior of complex social groups actually depends in part upon the influence of random noise. Again, I'm not an expert in the this area, but it's a pretty fascinating situation.