Hair materials and children

I am working on coloring hair. To do this, I have been learning how to use the Hair Info node to control where colors are placed on the hair (for example, use the Intercept factor of Hair Info as the Mix Shader factor mixing 2 Diffuse shaders to have it gradient between the two down the length of the hair. Usually done with a color ramp.)

What I want to know now is if there is any way to control how materials interact with children? Say I have a parent strand with children around it (imagine them clumped up.) If I use the Intercept as above, that lets me control color down the strand. But what if I wanted to control color perpendicular to the strand? In other words, have the strand be black, then gradient out to the children around it, with closer children being gray, and the furthest away white.

Is anything like this possible, or are the children just exact copies of the parents that cannot be affected in such a way?

The parent actually disappears and is replaced by the children, you can see this by flipping the number of children between 0, 1, and 2. The children each act as regular hairs as far as shading is concerned. As far as I know the stand-info node can’t get the info for this atm.

Thanks for the response. The parent can be rendered if you check the box for it. It is annoying to learn that there is not more options. I am trying to find some sort of way to do edge detection on particle hair, but to detect the edges of the clumps created from children around a parent (normaly edge detection stuff just picks up the individual strands.)