Challenge: Sunflower

I really want to figure out how to make this:

inspiration pic found online,
but no tutorial

So I think it's a bullseye with a brown center (you mix the 3 primary colors?) and yellow surrounding that, leaving a bit of white and then marbled green everywhere else.

Here's my first attempt and I am way disappointed, but it give me ideas about what to do next.

1. use better dyes, these were from a cheap kit
2. accordion the petals better and maybe double dye them with 2 shades of yellow?
3. avoid a white line around the center brown spot by dip dying it without banding there
4. create more of the white light effect around the petals by using more rubber bands?

5/24/13 attempt 1
now that's just sad :(

I'm working on try two, and using this try #1 to experiment with making shamrocks.

5/25/13 attempt 2
still pretty sad :(

Wow, did not work.  This time what I learned is:

1. I need to use a lot more dye.
2. I forgot that I wanted the yellow to go partway and the white to be only on the edge.
3. Maybe I will try doing the brown center after the yellow has completely dried?
4. And the brown is still wrong.  Maybe I will try coffee?