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
Simple combination of stripy squares with their negatively coloured counterparts
Source Firkin
Remixed from a design seen in 'Burghley. The Life of William Cecil', William Charlton, 1857. The tile this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
Geometric triangles seem to be quite hot these days.
Source Pixeden
To get the tile this is made up from select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Remixed from a drawing in 'Maidenhood; or, the Verge of the Stream', Laura Jewry, 1876.
Source Firkin
Just to prove my point, here is a slightly modified dark version.
Source Atle Mo
A seamless pattern the unit cell for which can be had by selecting the rectangle in Inkscape and using shift+alt+i
Source Firkin
Inspired by a 1930s wallpaper pattern I saw on TV.
Source Firkin
Not the Rebel alliance, but a dark textured pattern.
Source Hendrik Lammers
A repeating background with a look of paper. I have added some changes to PatCreator. Now you can share your designs by submitting them to a new gallery section. Start by clicking Edit with PatCreator above.
Source V. Hartikainen
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
Looks a bit like concrete with subtle specks spread around the pattern.
Source Mladjan Antic
Inspired by a drawing in 'Kulturgeschichte', Freidrich Hellwald, 1896.
Source Firkin
From a drawing in 'Cassell's Library of English Literature', Henry Morley, 1883.
Source Firkin
Abstract Arbitrary Geometric Background derived from an image on Pixabay.
Source GDJ
Embossed lines and squares with subtle highlights.
Source Alex Parker
The image depicts a seamless pattern made using a bird's face.
Source Yamachem
Dark, crisp and subtle. Tiny black lines on top of some noise.
Source Wilmotte Bastien
Green Web Background, Seamless tile.
Source V. Hartikainen