IF you wanna try some free simple fractal software, go to
this journal. You don't need to know the math behind
Maybe you would appreciate my
Chaotic series of fractal articles (<- click) if you have a little theoretical interest
Regarding deep zooms in the Mandelbrot set, if you check out my deviation
Cauliflowerfort and click the link under "Artist's Comments", from page 4 you can follow the entire zoom sequence in 28 steps
In
this journal you have some links to cool fractal animations I stumbled over at YouTube. Also check out the zoom videos in
this journal .. and from the middle of the nineties there is a fantastic TV program about fractals,
Colors of Infinity by Arthur Clarke
Really beautiful soundtracks by Pink Floyd