A lot of these have very striking color schemes, e.g.:

http://chaoticafractals.com/art/FarDareisMai

Are these colors mathematically generated, or by a the artist?

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.

It's not clear to me where on the scale between photoshop and fully automated this is. Maybe you could elaborate? What is your workflow like?

You can get some idea of the workflow here: http://chaoticafractals.com/manual/tutorials/basic_gnarl

It's a combination of choosing the colour palette, selecting a set of mathematical transformations (and their associated weights), etc..

Chaotica is iterated function system software: http://en.wikipedia.org/wiki/Iterated_function_system