How do you get into fabric design?

I'm interested in making the patterns that go onto fabrics, not the actual fabrication of the material. Textile and Fiber Arts majors tend to focus on things like weaving, embroidery, color dying, etc, which I'm not interested in. I don't want to make the fabric or actually put patterns onto fabric, I want to design the patterns. What kind of degree is necessary to make the designs that go on fabrics, wallpaper, wrapping paper, homegoods, etc? If you were designing the fabric for a handbag, would you work for the design house brand that makes the bag, or would you work for some sort of fabric company that the designer would approach? I think graphic design would be somewhat related, and I've taken some cles in this, but most graphic design programs tend to involve a lot of things that wouldn't be related to fabric patterns such as advertising, fonts, page layout, etc.