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I'm trying to manipulate an object in blender to replicate an effect that I was able to create manually. It's a 'noise' pattern on a surface. See this puzzle picture:

Puzzle showcasing desired effect

I've been successful in applying random points to the surface of more complex shapes and extruding these points along the normal of the source geometry, but I'm having trouble using these points to create a new mesh with the desired effect. I think I need to integrate the points with the mesh before I extrude these points, but extruding after a join has no effect.

Current state in Blender Trying to join vertices into source mesh

Maybe it would make more sense to apply as a texture to the source model? The desired output is a obj or stl file to eventually map CAM paths to the new texture.

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I think for something like that you'd want to use a cloud texture and a displacement modifier

enter image description here

The Size parameter on the texture would control the amount of bumps and lows and the Strength on the Displacement modifier would make them more or less pronounced

On a cylinder you'd probably want to remesh it to have more even faces before the displacement modifier

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