Julia
Pacific Views made me go and check the google logo for today, the birthday of scientist Gaston Julia.
When Mandelbrot enthralled everybody with his sets and the like, a few of us, experimenting with Fractint found that every point in the set corresponded to a Julia graph. I used to study this, so you would think I can give you a better explanation, but nooo!
Anyway, they are infinite, they have a lot of nice properties, fractal dimension of course, and a bunch of other things which escape me right now.
UPDATE: I remember! Back in the Lorente household, for those of you keeping track, I saw a document by Julia discussing his recurrent function and its general properties. A yellow, old paper. Can't remember much more than that though.