I never know how to feel about mathematically/programmatically generated art. Despite having done a bit myself, I never think it actually looks good or artistic.
I can appreciate the technology behind it, but I still don't find it artistic or appealing. It's also amusing how the reaction to "I don't like any generative art I've seen" is "We'll then you clearly haven't seen this one." For whatever reason, I get the same reaction when I tell people I don't like beer. They insist I try their favorite beer. This strategy hasn't worked.
The colour palette is selected by the artist.
The mathematical rules governing the fractal then uses those colours, mixing together different colours from the palette based on the mathematical transformation chosen.