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The petals are very close together while in the bud phase.  As they wrap around the center point, the petals are not on the same vertical line as their neighbors and do not draw up water from the same part of the stem.  Splitting the stem will draw up the color and stain the petals based on their position in the spiral.

For more information, go to the following website:  http://www.scientificamerican.com/article.cfm?id=bring-science-home-capillary-action-plant

And for additional images and detailed instructions:  http://pinappu.hubpages.com/hub/How-to-make-Rainbow-Roses-a-Step-by-Step-Guide#.