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
A monochrome pattern from a tile that can be had by selecting the rectangle in Inkscaope and using shift+alt+i
Source Firkin
This is lovely, just the right amount of subtle noise, lines and textures.
Source Richard Tabor
The tile this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i
Source Firkin
Another fairly simple design drawn in Paint.net and vectorized in Inkscape.
Source Firkin
ZeroCC tileable stone texture, edited from pixabay, CC0
Source Sojan Janso
The rectangular tile this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i
Source Firkin
A seamless background drawn in Paint.net and vectorised with Vector Magic. The starting point was a photograph of drinking straws from Pixabay.
Source Firkin
From a drawing in 'Studies for Stories', Jean Ingelow, 1864.
Source Firkin
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Thin lines, noise and texture creates this crisp dark denim pattern.
Source Marco Slooten
This was formed by distorting an image of a background on Pixabay.
Source Firkin
Number 5 in a series of 5 beautiful patterns. Can be found in colors on the submitter’s website.
Source Janos Koos
Alternative colour scheme for the original floral pattern.
Source Firkin
Submitted by DomainsInfo – wtf, right? But hey, a free pattern.
Source DomainsInfo
A background pattern inspired by designs seen in 'Burghley. The Life of William Cecil', William Charlton, 1857.
Source Firkin
Remixed from a drawing in 'Hungary. A guide book. By several authors', 1890.
Source Firkin
Remixed from a drawing in 'Maidenhood; or, the Verge of the Stream', Laura Jewry, 1876.
Source Firkin
The tile this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i
Source Firkin
The tile for this is based on a repeating unit close to a design on Pixabay. It can be had by selecting the rectangle in Inkscape and using shift-alt-i.
Source Firkin
Seamless , tileable CC-0 texture. Created by my own, feel free to use wherever you want!
Source Linolafett
The tile this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i
Source Firkin
The rectangular tile this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i
Source Firkin
Luxurious looking pattern (for a T-shirt maybe?) with a hint of green.
Source Simon Meek