Blender 3.1 notes: using texture maps for particle hair

First, set up the hair particle system with enough to see what you’re doing.

In the UV Editing tab, create a new image and change the Colour Space to Non-Colour.

Save the image either with Alt+S or using the Image menu.

In the particles tab, select the particle system you want to use the texture for, then scroll down to Textures. Create a new texture in one of the slots.