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Is there a way to do this with material nodes only?

I can find a particle info node:

https://docs.blender.org/manual/en/latest/render/shader_nodes/input/particle_info.html

But the object info node doesn't have an input... the texture coordinate node does have an input for a different object, but then I can't find the distance node:

https://docs.blender.org/manual/en/latest/editors/texture_node/types/converter/distance.html

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The distance node is part of the (kinda-deprecated) texture node editor, which is different from the shader node editor. To get the distance between two locations, use a vector Math node set to Distance.

enter image description here

Result :

enter image description here

Note : The shader should go on the particle object, not on the instancer.

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    $\begingroup$ Superb! Easier than I thought, but impossible for me as a beginner to figure out on my own (especially with apparently outdated documentation). Thank you so much! :) $\endgroup$
    – eobet
    Commented May 19, 2020 at 14:40

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