The shader for the horizontal tubes alone is trivial. Just plug the density into the transparency channel. I won't even bother demonstrating that.

So - what to do about both sets of fibers.

Observe how the horizontal ones interrupt the gaps from the vertical ones.

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Renderosity forum reply notifications are wonky. If I read a follow-up in a thread, but I don't myself reply, then notifications no longer happen AT ALL on that thread. So if I seem to be ignoring a question, that's why. (Updated September 23, 2019)