Make a skinner blend using the photo below as a guide. You want some plain white on one end so make sure it hangs over the red. If you've never made a skinner blend before, see here for a really great tutorial. Stop when you have a long, thin strip.
Lay your blended strip out on the work surface. Trim the white end so it is straight across.
Extrude some skinny black strings.
Lay a few strings across the white end of the blend as shown.
Fold the strip back over itself about 2 inches from the end (less if your strip is smaller). Add a couple more strings.
Keep folding the strip back and forth, accordion style, adding 2-4 black strings between layers, until you run out of strip.
Carefully compress the stack from the middle out on all sides to expel air and get it into more of a square log shape. Reduce it until the ends are about 1-inch square.
Cut the log in half...
And re-assemble with the red sides in the middle. (Or you could reverse it to have red petals with white down the middle.)
Compress the two halves and reduce into a long, round cane.
Cut it into 6 equal pieces.
Pinch the pieces in petal shapes.
Add a really thin sheet of black clay to one half of one side of each petal as shown and set aside.
Make a small white log and cover with a thick sheet of black clay.
Reduce to about 1/4 inch or smaller. Put all of the pieces together as shown below.
Roll out a medium-thick sheet of translucent clay. Wrap it around the cane, using a needle tool to press it into the creases.
Add wedges of translucent clay between the petals. Make them big enough to stick out beyond the points of the petals.
Trim the wedges so that the whole thing is as close to a cylinder shape as you can get.
Reduce your cane. Let it rest at least a couple of hours (if you can wait that long) before cutting into it and seeing your work.