I recently started developing an interest in fractal art. I found a very cool, free program called Apophysis that allows Me to create my own pieces. Unfortunately, the most recent release of the most popular version, 7x, won't run on My laptop for some reason. (Oh, the joys of open-source.) However, there's an older version that lets Me do most of the same things, including create 3D images, which does work for Me.
Here are a couple of My first attempts. Not fabulous, but I'm learning.