How can I align a texture and material based on the same image?

Question

I am trying to model an "inflationary multiverse", inspired by this picture from Quanta Magazine:

To do that, I am trying to create a bunch of bubble universes expanding out as part of the same space-time manifold. I can get a nice shape for this by using the displacement modifier based on a texture based on this Voronoi image:

So far so good. But now, I want each of those bubble regions to have its own distinct color. I thought that I would be able to accomplish this by taking the same Voronoi image and manually coloring the regions as follows:

But when I try to apply a material based on that colored image to the mesh, the displacement pattern and the colored patches do not align :( Here is what you get by default:

I somewhat understand how the 512x512 colored image is mapped to the icosphere via UV-unwrapping, but it's not at all clear to me how the 512x512 black-and-white Voronoi image is mapped to the texture that is in turn mapped to the icosphere (the texture settings do not seem very configurable). Is there a clean way to get the texture and material to align?

The file is here:

Answer 1

In your blend file, you have coordinates set as "local" instead of UV. That seems to be the issue (if I understand correctly).

Also don't forget to pack resources, so we can see the external data.