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I am trying to create an array of lamps that would light up one after another in a constant interpolation. The problem is that I can't figure out how to UV unwrap the lamps so that only one lamp would be entirely white at a time, and so that I could animate ColorRamp arrows and move the "light" from one lamp to another. Hope it makes sense.

I tried to unwrap them together and separately but to no avail. Any suggestion would be appreciated

This is what I am trying to achieve enter image description here And this is what I am getting enter image description here

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You can select all your object, switch to Edit mode, choose the top orthographic view and unwrap from view:

enter image description here

Then in the UV Editor enable the Pivot > Individual Origins and scale down the islands a lot:

enter image description here

Give your objects this node setup, with a Separate XYZ, in order to project a white stripe on the good axis:

enter image description here

Then animate the Mapping node Location values so that the stripe moves along the good axis:

enter image description here

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