since the non-linear equations used to define the lorenz attractor actually produce a three-dimensional graph (rather than a flat image), here’s a model created by geoff milburn to help visualize the phenomenon.  he explains:

“This is a rendering of the long journey of a single point in Lorenz’s creation, a path consisting of three million iterations developed in Processing that shows the region of allowable values in the model more clearly. Older values are darker, and the visualization is animated to show the strange dance of the current values of the system as they sweep from arm to arm of this dual-eyed mathematical monster, order generating chaos.”