Scott Hotton's Fractal Gallery 
These are Julia sets for rational functions of the complex plane that are obtained by an operation similar to Netwon's method. This is a useful way to custom design Julia sets because you can specify the locations of super stable fixed points for the rational function. Click on a picture to see a larger version. 
Click on the picture to see the animated Julia set.

These are histograms of chaotic attractors for noninvertible functions of the plane. Like functions of the complex plane the structure of these attractors is strongly influenced by the critical set. However unlike functions of the complex plane whose critical sets are discrete the critical sets for these function are curves. Near the critical curves the functions compress regions of the plane. Therefore there is a higher probability of finding points around the images of the critical curves. This creates the structure one sees in the histograms. For more information on this subject see the book that I illustrated, "Chaos in Discrete Dynamical Systems" by Ralph Abraham, Laura Gardini, and Mira. Click on a picture above to see a larger version. 

