Complexity arises when a system can't be reduced to the simple mechanistic models that science usually uses. Whether or not these systems - such as the weather - are ultimately deterministic, if only you have enough information and the right theories - is a matter of debate. The Nobel prize winning Chemist Ilya Prigogine, who is known for his work on complex systems, said that "The more we know about our universe, the more difficult it becomes to believe in determinism."
Also of interest is the idea of Emergence, which is the arising of complex systems out of simple ones. The way that new properties appear that do not seem to be explicable purely in terms of the interaction of the simpler components. Again, this a matter of debate. I call this characteristic Uranus, the creative principle, where new elements emerge in your life that you could not have thought of and that are not just a re-arrangement of the old.
