It wasn't too long before I started looking for other programs to try. I came across Ultra Fractal, software written by Frederik Slijkerman, which is based on the earlier open source program, Fractint. Ultra Fractal was a windows-based program which is now also available for Macs, that allows for multiple layers and much more powerful rendering capabilities, giving the user far greater artistic control.
Over the years Frederik has further developed the complexity of the software, with the help of a core number of well-known formula writers. It is probably the most widely used fractal-generating software today, and the one I still use now. It is available to try for free here: Ultra Fractal