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I'm working on a procedural texture that generates a field-line pattern like you might see in diagrams like this: An example of Field Lines

Requirements

The arrow heads aren't important from that diagram. I'd like to have control over the thickness and the number of field lines displayed. They also should not be constant thickness along their length, i.e. they should be wider the further from the charges they get.

What I've tried so far

My first thought is to create some angle based gradient around each node that can then be stratified, like follows. enter image description here enter image description here enter image description here

The charges in the field diagram are included in the material with the Combine XYZ nodes on the left.

From here, it's clear that this gradient needs to be augmented somehow using the distance from each node to curve these lines toward each node. Unfortunately, I'm unable to figure out a way to blend these gradients that gets the desired result of curving the black and white lines toward the 3 nodes.

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