Last week I got the inspiration to play around with fractals. After spending searching for a suitable program, I settled with Ultra Fractal. The software is not free, but it feels intuitive to use and has an extensive library of public formulas. It costs between 29 € and 99 € depending on the version. I would recommend getting the mid-tier Creative Edition as it comes with layers feature similar, allowing merging multiple fractal formulas. The most expensive version adds animations and the possibility to use several computers for rendering.
The Trinity below is my first creation and consist of two Mandelbrot and two Newton fractals mirrored vertically. The Mandelbrot sets form the main features and Newtons are used as background features. Newton fractals are also rotated around the origin. Pawn, Launch and Nova, are zoomed in parts of the main image.
I also installed Frax on my phone. The app has a minimalistic UI and only creates Mandelbrot or Julia fractals, but produces beautiful images by default. It is easy to use gestures to move around the fractal and change colours, lighting and textures. Additional controls can be unlocked as an in-app purchase, but I have not tested them yet. The results can be exported in a decent resolution, and high-quality cloud rendering is available at additional cost. Below are two quick renders using the phone.