I have a question for you. I am not sure if I can understand strange attractors and how they are related to chaos. I'll try . Let's look at the logistic map. This is one of the most basic basic systems used to demonstrate chaos.
All initial points end up converging to one of the values.
The basins of attraction are the sets of intial starting points that end up at each. The interesting point here is that these basins can have really weird structures. There are regions intermixed. A first there is a point that goes to attractor B first. No matter what scale you look at.