say we start with a set of points uniformly distributed in a disk:

what happens when we map this set of points forward by the Henon map:
x_n+1= 1.4-x_n² + .3y_n
y_n+1 = x_n

Here's a Quicktime movie that illustrates how quickly the set converges to the attractor and how quickly things get mixed within the attractor.
Henon movie