Regardless of how you choose to do it, if you've never done it before, you really should give it a go! Creativity is liberating and can work wonders on your soul. Retreating into your own mind and getting lost in colors or shapes and expressing them through movement or form is an amazing experience.
I used to paint quite frequently, as a young girl. Oils were my favorite medium. Then I switched to drawing & coloring with pencils. Now, my medium of choice is my computer. Whether I'm creating fractals or more familiar graphics, the time I spend making art is transcendental for me.
My favorite software for creating digital art is Corel's Paint Shop Pro X5 (PSP). I used Jasc's Paint Shop Pro 9, far past its prime, before finally giving in and switching but, I'm glad I did. What prompted me to switch was Corel adding my favorite feature to the native plugins: randomize. This is especially fun to play with when using kaleidoscope (just remember to save your favorite settings). It is a very useful feature for many others, as well. (If you would rather have free graphics software, I have heard nothing but good things about Gimp.)
A search for "fractal art generator" in a search engine will give you enough names to get you started; however, Ultra Fractal and Apophysis are among the most popular, with Apo, as it's called, being the easiest to use. No matter which program you choose, though, you can find groups, plugins, tutorials and whatever else you need for help with learning how to use it on DeviantArt. Researching it there will also allow you see the types of images that the various programs are used to create.
How do you like to express your creativity or, if you never have, how would you like to?