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I'm trying to duplicate the following type of gradient like the horns in this picture:

bull horns

I saw an example of that uses a texture as a transition, but it only shown just a duo-tone gradient using a gradient texture. I want to know if is possible to either influence the stops on a color ramp or modify the technique mentioned in the link to get the desired effect?

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It's time to dig this up and make it right.

Final

final

Object and UV Map

Create your horn using chosen technique and UV Unwrap it with Follow Active Quads as in my answer here: How to Straighten Curved UVs into Straight Belt

Using this method is somewhat crucial as we need to have UV Map straighten to X axis.

objects

Material

Extending a bit setup from your link we will make 3 maps. Base color, Roughness and Normal than use them with Principled Shader.

For Base color we mix main gradient with light and dark spots.

For Roughness and Normal we will use stretched and mixed Noise Textures.

mix

Most important things here are Mapping nodes with stretching along X and Y axis.

Nodes

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