Wada - minus the reflecting ballsNormally, symmetric fractals doen't possess the type of arresting, intriguing beauty of the asymmetric ones. Wada basin fractals, which are often symmetric, do have a unique visualization that I find more aesthetically appealing.
Perhaps the best thing about Wada basins is that they can be simulated with easy-to set-up lighting and symmetric arrangements of reflecting balls - e.g. Christmas ornaments. Some instructions for doing this are at The Optical Gasket Lab , a fun module from the Yale Fractals course designed by M. Frame and B. Madelbrot himself.
The real instantiation of the basin boundaries allows for interesting comparisions of these real optical images and computer-generated graphics. See the Secret Inner Life of Mirrored Spheres: Wada Basins by Miquel.com for a set of beautiful images. (The image at the top of this post is from this site)