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I've got these eyebrows made with a Hair Particle System using Interpolated Children. I would like to fade each hair particle as it gets further from the base. Red line is the base, green is where it would be fading to transparent.

So far, I have the particles so the base is thicker than the end which is good, but I want to fade them out even more. The material is pretty simple, just a couple of BSDFs mixed together.

I've tried to mess with Texture Coordinate or Particle Info with a ColorRamp as the Fac on a MixShader between a Transparent BSDF and the Hair Material, but it has only affected the entire particle systems, not individual particles in the system.

I am planning to render this in Cycles, so it would be nice if the solution worked in it.

Eyebrows

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To get a gradient from the root of the hair to the tip you can use a Curve Info node in the Shader Editor. You'll find it under Shift+A > Add > Input.

The Intercept output gives a gradient from 0 to 1 starting at the root and ending at the tip. To show this, I plugged it in a Color Ramp going from red to green like you showed in the question:

hair gradient color

This is just a Principled BSDF using it for the Base Color to color the hair, but you could also plug the (inverted) Intercept value into the Alpha input to make it slowly transparent.

Or if you are going to use a Principled Hair BSDF instead, this has no Alpha input. In this case you can use the Intercept value as a mix factor to combine it with a Transparent BSDF:

mix hair with transparent

Now it is up to you to tweak the settings until you find something you like.

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