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There are several free fractal generating programs out there (Apophysis, Mandelbulb 3D, and Fractal Explorer...just to name a few). After installing them, you then have to teach yourself how to use them - but there are great tutorials, resources, on dA, and out on the web.
The formula's are already built into the software - so you don't even have to understand the math behind it. But if you do, some of the programs let you edit the formulas and just play.
I am in the group that has a very limited understanding of the math, but have taught myself how to use the programs to 'find' interesting images. However, I go a step further. You will notice most of my submissions are in the category 'fractal manipulation'. This means i take a fractal image and will manipulate it in other software, like Photoshop.
Hope this helps!
Take care!!
wish mine looked so beautiful.