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
Seamless pattern the tile for which can be had by using shift-alt-I on the selected rectangle in Inkscape.
Source Firkin
From a drawing in 'In an Enchanted Island', William Mallock, 1892.
Source Firkin
I guess this is inspired by the city of Ravenna in Italy and its stone walls.
Source Sentel
This one is quite simple in design, it consists of vertical stripes layered on top of a seamless texture.
Source V. Hartikainen
To get the tile this is based on select the rectangle in Inkscape and use shift-alt-i
Source Firkin
It almost looks a bit blurry, but then again, so are fishes.
Source Petr Šulc
An emulated “transparent” background pattern, like that of all kinds of computer graphics software.
Source AdamStanislav
A repeating background of thick textured paper. Actually, it turned out to look like something between a paper and fabric.
Source V. Hartikainen
Prismatic Basic Pattern 2 No Background
Source GDJ
The image depicts a seamless pattern of a fishnet with a plenty of fish.It may be a lucky charm for fishermen.
Source Yamachem
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
From a drawing in 'Art Embroidery', M.S. Lockwood and E. Glaister, 1878.
Source Firkin
A seamless pattern formed from a tile that can be had in Inkscape by selecting the rectangle and using shift+alt+i.
Source Firkin
From a drawing in 'Uit de geschiedenis der Heilige Stede te Amsterdam', Yohannes Sterck, 1898.
Source Firkin
From a drawing in 'Sun Pictures of the Norfolk Broads', Ernest Suffling, 1892.
Source Firkin
From a drawing in 'Royal Ramsgate', James Simson, 1897.
Source Firkin
From a drawing in 'Heroes of North African Discovery', Nancy Meugens, 1894.
Source Firkin
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
This is lovely, just the right amount of subtle noise, lines and textures.
Source Richard Tabor
Formed by distorting an image on Pixabay that was uploaded by gustavorezende. To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
More tactile goodness. This time in the form of some rough cloth.
Source Bartosz Kaszubowski
Seamless pattern formed from a tile that can be had by selecting the rectangle in Inkscape and using shift-alt-i.
Source Firkin