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I recently started learning Adobe Illistrator and I'm trying to make a gradient follow a loop. From what I could find online, I've learned how to make a gradient follow a path, but I can't find anything that involves a path that overlaps in a loop. What I have in mind is something like this, where the gradient follows the red arrows and continues to follow the path as it goes behind the base of the loop. This is just to illistrate what I have in mind, it's not the result of any of my attempts I tried making a path using the Line Segment and Arc Tools, and then joining them (in the order that I want the path to go, not all the segments at once), but the resulting gradient didn't run smoothly along the loop. Then, I tried using the Pen Tool to make the loop and connecting it to line legments at the beginning and end of the loop, but that didn't yield a result either.

As I am rather new to Illistrator, I'm not quite sure what else to try. Any suggestions would be appreciated.

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If it's a single path with a stroke, using the Apply Gradient Along Stroke in the Gradient Panel should work.

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If it's not a stroke, and is a shape with a fill then matters are more difficult. Generally, a Gradient Mesh would work best. But it's complicated. Meshes can become unruly and hard to edit/apply to an existing, non-rudimentary, shape. In fact, for a filled shape such as your loop, it can often be easier to start with a gradient on a stroke, then use Expand Appearance which will result in shape with a gradient mesh fill.....

enter image description here

... otherwise I'd create a long thin strip, apply a Gradient Mesh, then distort the strip into the loop, which is by no means an easy thing to do well, even for experienced Illustrator users.

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