How to get started with building a robot/machine that can draw art?

I want to build a robot/machine that can draw art. It doesn't necessarily have to be a robot arm that uses a drawing utensil - for example there could be some type of lattice over the top of the drawing surface and you could then control the x/y of the drawing component.

What should I start learning for a project like this?

I'm an experienced programmer but I mainly do web development. I know C/C++.

You might search the forum for CNC and plotter as these may provide useful info. You will need to figure out how to feed "art" into the arduino. Is this for an art class/project?

Thanks, CNC and plotter were very helpful. It's just a personal project - not for a class.