Fractal formulas can create astonishing things. A lot depends on how the particular program renders them though. The above image was made in InkBlot Kaos, one of a number of programs made by the well-known fractal programmer, Stephen Ferguson.
I particularly like InkBlot Kaos because I can made interesting things quickly and relatively easily but also explore variations in coloring and formulas just as easily. This image uses the following formula entered into its simple formula parser: "atan(atan(2*(c))-(3.2^z)+c)^4"
I just made it up by playing around with numbers and the few trig things that it allows. The possibilities are huge, particularly if you like to experiment with things like I do.
Below is the original image as it was rendered in the program.
I don't make the images, really; I just push buttons and turn dials. That's the other thing I like about fractal programs.
Here's a variation of the very first image which was India Inked. I used the Mirror-Mirror filter. Mirroring seems to work well with fractals as they have a lot of wild detail and the mirroring gives them a nice ordered and polished look.
Sometimes I think of fractal programs as art slaves because their creative contribution is so much greater than mine. An equally accurate description of them is that they are quite simply just a very powerful tool for the production of creative imagery. Art Slave sounds sininster, brutal, oppressive, maniacal. It conjures up images of chains, whips, endless toil without goal or profit -- one's very offspring snatched from their hands and sold like cattle for a cruel, uncaring elite.
I can assure you, there is absolutely nothing like that going on in the production of fractal art.