chaos and random? what's the difference?

Question

Hello:
Could somebody explain me what is the difference (if any) between a chaotical behaviour and a random behaviour? What I know is that, for example, a butterfly path is chaotic, also, the path of the smoke of a cigarette, and the diffusion of a drop of ink in a glass of water, because in all these cases you can't predict how the particles (or objects) will move. That seems to be random, isn't that? Thanks

Answer 1

Chaos, in science, actually means extreme sensitivity to intial conditions. Random means that there is one or more parameter that lacks any dependence on initial conditions. Neither can be predicted, but for different reasons. A chaotic system generally cannot be predicted because it is impossible to measure the initial conditions with sufficient accuracy. A random system cannot be predicted because nothing that is known about the system is useful in determining at least one parameter of the future state. If a chaotic system were reproduced with identical initial conditions (which is impossible due to the extreme sensitivity), it would have identical results because it really is deterministic. The same is not true of a random system.