I for one always get confused when trying to distinguish the difference between randomness and chaos. So the following is an attempt to understand these.
A chaotic system is a complex nonlinear system that is highly sensitive to initial conditions. These systems are not random/disordered but are ruled by a deterministic behaviour. Simplified models of such systems generate erroneous results as initial errors accumulate during iteration.
So... in other words ‘chaotic’ systems are just highly complex and cannot be modelled accurately using simplified models or approximated initial data. They are simply called chaos because back in the age scientists couldn’t deal with such complexity and assumed that the system was unpredictable.
In contrast, the random walks we’ve been looking at this week are not individually predictable but are associated with a probability distribution. However using this distribution, predictions can be made about the properties of a collection of random walks.