I've been wanting to do some donut as well as large tube shaped polymer beads, and here are some black and white ones I just made. I was inspired by the mudcloth technique in Judy Belcher's book, Polymer Clay Creative Traditions. She has two interesting techniques for mudcloth in her book, but I improvised a little from her technique.
I carved the designs using a linoleum cutter v-gouge. I'd like to find a better quality carving tool as I want to do more precise designs than the tool let me do. But in trying to recreate the primitive African tradition of mudcloth, it looks pretty close.
One hint for success: if you want to carve through to an underneath color, make sure your top sheet of clay is reeeally thin. As thin as you can make it.