I saw some radical borders recently. A border is at the edge of a 2-dimesional piece....the border can be all around the rectangular edge, or it can be at the bottom of a piece of fabric - as say, a curtain, or a drape, or a skirt or an apron - or, it can simply be at the top and the bottom, as in some tiles, or it can be simply at the top, as in say, a letterhead for your stationery.
Borders can be geometrical, or picturesque, colorful, or simply graphic in one or two colors, representational or abstract, or from a certain culture, or historical, or thematic, or simply technical and whimsical.
The borders I saw were done in fused glass, and they hung in a window, so the light could flow through the colors. In a rectangular shape about 8" by 4", they seemed to be a series of stripes interspersed with bubbles; definitely whimsical and evoking a certain mood. The whole piece was stripes, in fact, (see a previous entry) but they were obviously borders, placed all in a row, one on top of the other, as in a sheet of paper: definitely two dimensions!