Chaos theory is a very challenging and interesting concept which you should check out, but one of the most mundane outcomes of it is that there is no way to predict the physical world. No way to see what is going to happen. Now, obviously one could predict a simple neutonian mechanical system for a 10 second-period, or predict enough of electrical impulses in a piece of designed silicon to make a functional processor - but in general, in the widest sense, there is no way to predict the universe. Even with the assumption that there is some completely determined process at the microscopic core of every interaction - those processes, when combined into big systems, wired up with feedback loops and put in a system so tiny that one has to had a machine 2 times bigger than the original system in the first place: and we arrive at total unpredictability of the universe.
Note, this is not just practical unpredictability: the question is not about us not having enough technical prowess to predict the universe. The issue is that it is physically impossible to build any real prediction machine that would predic the whole thing: you would need a bigger universe than the universe it is trying to predict. It is even a logical contradiction!
Thus determinism becomes more of a philosophical outlook than an actual physical property that could be calculated, predicted etc.
Even the word itself - "determinism". Assumnig that the fate, the outcome of something is determined. In what way can it be determined if we know that it is physically impossible to determine it? Not because we lack machines or havent built a strong enough microscope. Our very own scientific paradigm, the scientific method, the way of thinking about the universe - the thing that lies at the core of our worldview - says that it is impossible to predict the whole system. Absolutely impossible. So it is unpredictable - ergo undetermined.