Colour By Numbers
I rendered these images with a freeware fractal flame editor called Apophysis which you can download from here. They were rendered with version 2.05 beta 2 on my Pentium III 2.8G Windows/Intel based machine. Of course, having multicore and the newer embellishments for your processor and memory/bus bandwidth will considerably beef up performance and reduce render times. There is a great deal of mathematics involved in fractal geometry, and it is worth the time to read the documentation and feel free to experiment with the parameters.