I was hoping for something more like the “Mandelbulb”.

Sticking to just the “regular” mandelbrot, aheight map based on escape iteration is fairly obvious given the algorithm, and there are a few techniques for getting better results.

Another alternative is to make the center pop out somehow. One example is on Wikipedia: https://en.wikipedia.org/wiki/Mandelbrot_set#/media/File:MandelbrotOrbitInfimum.png