You might know the logistic map, with its attractor, which depends on the map parameter like so (shown is the most interesting region, where r is between 3 and 4):

Uh. That is the common way it's presented, and it's quite ugly, because you can't see that much in the chaotic regions. I made a neater version, available as a huge image file (8000 x 8000 pixels). Make sure you zoom in and notice how all the chaos joins together into the sudden islands of stability.