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Interestingly enough, titsmurf's theory was pretty much the norm before Einstein's theories about quantum mechanics; reality is deterministic and "mechanical" (in the sense that our actions are always the same).
After Einstein, we started to realize that the world is anything but deterministic. After all, if sub-atomic particles move randomly, and can even appear and disappear at any time, in any place, how can a combination of those particles (a human, for example) be deterministic? Your brain works with electrons, which randomly choose a route through your brain's pathways. Because this happens at random, it is possible that you'll make a different decision every time you were to "rewind" time to look again. Of course, because of the increased "bandwidth" of often-used pathways, it is likely you'll make the same decision time and time again. Just like it is likely replicated DNA is exactly the same as the original; there is a small chance that a mutation will occur, and this small chance leads to the diversity in present day nature.
This same randomness of reality leads to variations in local wind-speed and direction, variations in spin of a thrown rock, variations in movement of birds, and everything else.
As for your last question, about the giant formula: it's called the "theory of everything", and it's pretty much the holy grail of mathematical physics. It is unlikely this formula will be deterministic.
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