Not strictly seamless in that opposite edges are not identical. But they do marry up to make an interesting pattern
Source Firkin
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
A huge one at 800x600px. Made from a photo I took going home after work.
Source Atle Mo
Number 5 in a series of 5 beautiful patterns. Can be found in colors on the submitter’s website.
Source Janos Koos
Similar to original, but without gaps in between the arrows. This seamless pattern was created from a rectangular tile. To get the tile, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Remixed from a drawing in 'Chambéry à la fin du XIVe siècle', Timoleon Chapperon, 1863.
Source Firkin
This was formed by distorting an image of a background on Pixabay.
Source Firkin
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Seamless Prismatic Pythagorean Line Art Pattern No Background. A seamless pattern that includes the original tile (go to Objects / Pattern / Pattern To Objects in Inkscape's menu to extract it).
Source GDJ
Looks like an old wall. I guess that’s it then?
Source Viahorizon
Luxurious looking pattern (for a T-shirt maybe?) with a hint of green.
Source Simon Meek
From a drawing in 'Two Women in the Klondike', Mary Hitchcock, 1899.
Source Firkin
Prismatic Abstract Background Design
Source GDJ
White fabric looking texture with some nice random wave features.
Source Hendrik Lammers
One more updated pattern. Not really carbon fiber, but it’s the most popular pattern, so I’ll give you an extra choice.
Source Atle Mo
Classy golf-pants pattern, or crossed stripes if you will.
Source Will Monson
Geometric lines are always hot, and this pattern is no exception.
Source Listvetra
A seamless pattern formed from a modified version of rwwgub's tile. To get the tile, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Formed from a tile based on a drawing from 'Viaggi d'un artista nell'America Meridionale', Guido Boggiani, 1895.
Source Firkin
Heavily remixed from a drawing in 'Barbara Leybourne; a story of eighty years ago', Sarah Hamer, 1889.
Source Firkin
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
Design drawn in Paint.net, vectorised using Vector Magic and finished in Inkscape.
Source Firkin