Through infinite iteration, we will eventually end up with a set of points that remain in the Cantor Set. (They are not 'thrown out' in one of the middle thirds intervals.) Thus, a graphical representation of the set will consist of a 'dust' of scattered , unconnected points that make up the Cantor Set.
So what does this set have to do with chaos? It just so happens that certain functions, when iterated many times, produce effects that are similar to that of the Cantor Set. For instance, consider the logistic function f(x) = 4.5x(1 - x) mapped over the interval between 0 and 1 on the real number line. With every iteration of this function, the middle third of the x values are 'thrown out' of the interval [0, 1], so the effect is that only the points within the Cantor Set will stay in this interval whe n iterated through the function. (All others will escape the interval.) The concepts of staying within an interval and escaping an interval will help you to understand complex sets such as the Mandelbrot Set.