The Lorenz attractor near an intermittent cycle: much of the time the trajectory is close to a nearly periodic orbit, but diverges and returns. Change the parameters slightly and the intermittency will either dissolve or turn into a real attractive periodic cycle.
<a rel="nofollow" class="external text" href="https://www.flickr.com/people/87547772@N00">Anders Sandberg</a> from Oxford, UK
CC BY 2.0
<a rel="nofollow" class="external text" href="https://www.flickr.com/photos/arenamontanus/273180669/">Intermittent Lorenz Attractor</a>