Generate css colours for categories

Hi!
Im currently developing my own theme.
Now I want to have a specific colour for each category dynamically generated in my css file.

It’s quite important that it’s generated dynamically because I want people to easily add categories without editing the css. So once a category is added it gets its unique colour.

The point I’m struggling with is how to code a php function that generated a css valid colour for each category and writes that in my css file.
Even better: I would just use following ‘base colours’ red, green, blue, and black and certain respective shades if there are more than 4 categories.

I hope I made clear what I want to do. Thanks a lot in advance!!