Blender hair texture not influence clump

Does anyone know how hair texture influence work?
I try to use a texture to affect children hair clump, but it not change anything follow
the texture. It can still affect hair density and length.
I attach the file below.


The result I desire should look like this with texture influence only

The file:
hair clump.blend (1.7 MB)

Here, I just had to set clump value in Particle System settings to 1, to have it working in your blend file.

The BW image is basically a way to locally multiply this value.
If clump value is 0, whatever is the pattern is on texture, clumping is null.
But if clump value is set to 1, you should see difference between use of texture and absence of texture.

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Thanks. The hair mostly focus on the hair guide, not really same as I imagined. Seem thats how it work in Blender