Well, below there are some recycled info:
Wikipedia has a nice site
[link] Most software can be downloaded from
[link] . Many progs are free, for example Fractal Forge, Xaos, and Fractal Explorer
Not so difficult to play with such progs. You don't have to know anything about the math behind (most fractal artists do not). Otherwise you can have my "Chaotic series of fractal articles"
[link] as a resource
Regarding deep zooms in the Mandelbrot set, if you check out my deviation "Cauliflowerfort"
[link] and click the link under "Artist's Comments" you can follow the entire zoom sequence in 28 steps
In my journal
[link] you have some link to short cool fractal animations I stumbled over at YouTube