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
More in the paper realm, this time with fibers.
Source Jorge Fuentes
A background pattern inspired by designs seen in 'Burghley. The Life of William Cecil', William Charlton, 1857.
Source Firkin
Light gray grunge wall with a nice texture overlay.
Source Adam Anlauf
This is the remix of an OCAL clipart called "Rain on Window" uploaded by "pagarmidna".Thanks.This is a seamless pattern of raindrops.
Source Yamachem
Formed from a tile based on a drawing from 'Viaggi d'un artista nell'America Meridionale', Guido Boggiani, 1895.
Source Firkin
Remixed from an image that was uploaded to Pixabay by Pixeline
Source Firkin
Imagine you zoomed in 1000X on some fabric. But then it turned out to be a skeleton!
Source Angelica
Design drawn in Paint.net, vectorised using Vector Magic and finished in Inkscape.
Source Firkin
Hexagonal dark 3D pattern. What more can you ask for?
Source Norbert Levajsics
Lovely pattern with some good-looking non-random noise lines.
Source Zucx
Vector version of a png that was uploaded to Pixabay by pencilparker
Source Firkin
I took the liberty of using Dmitry’s pattern and made a version without perforation.
Source Atle Mo
From a drawing in 'Codogno e il suo territorio nella cronaca e nella storia'', Gio and Giarella Cairo, 1897.
Source Firkin
Another fairly simple design drawn in Paint.net and vectorized in Inkscape.
Source Firkin
Not sure if this is related to the Nami you get in Google image search, but hey, it’s nice!
Source Dertig Media
A seamless pattern the starting point for which was a 'colour modulo' texture in Paint.net.
Source Firkin
CC0 and a seamless pattern from a tile drawn in Paint.net .
Source SliverKnight
Sometimes simple really is what you need, and this could fit you well.
Source Factorio.us Collective
Prismatic Curved Diamond Pattern 6 No Background
Source GDJ
Just to prove my point, here is a slightly modified dark version.
Source Atle Mo
Prismatic Curved Diamond Pattern 7 No Background
Source GDJ
Remixed from an image on Pixabay, the original having been uploaded by darkmoon1968.
Source Firkin
Medium gray pattern with small strokes to give a weave effect.
Source Catherine
This was formed by distorting an image of a background on Pixabay.
Source Firkin