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To generate seamlessly looping noise in Audacity:

Generate your favorite type of noise. If you want to apply filters/EQ, do it now. If so, trim several seconds from the start and end of the filtered noise to make sure there are no audible boundary effects from the filters acting on the start or end of the noise.

Duplicate the noise twice, so you have three copies of it, all on separate tracks. Drag track 3 to the right until the beginning of it snaps into alignment with the end of track 1 (watch for the yellow line; it's very important to align all the edits correctly). Drag track 2 somewhere in the middle.

Using the auto-snapping again, select both tracks 1 and 2 in the part where they overlap (drag across both, using the auto-snapping to align the selection. You should see two yellow lines). Use the "Crossfade Tracks" effect with a "Constant Power" fade type to crossfade tracks 1 and 2. Do the same for the part where tracks 2 and 3 overlap.

Select the beginning part of track 1 where it plays alone (snapping with the yellow line again) and also the empty space below it (drag down). Delete this. The tracks should all stay in alignment. Select and delete the ending part of track 3 where it plays alone too. Mix all the tracks together using Tracks, Mix, Mix and Render.

If you loop the result you get effectively 2 copies of the noise playing simultaneously but out of phase, repeating indefinitely, very slowly crossfading in and out, and with the loop point of each copy set at zero volume so you can't hear it.