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 beautiful dark wood pattern, superbly tiled.
Source Omar Alvarado
Feel free to use this seamless background texture as a background on a web site. It's colored in a light pink color and is seamlessly tile-able.
Source V. Hartikainen
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
A seamless pattern formed from a square tile. The tile can be retrieved by selecting the rectangle in Inkscape and using shift-alt-I.
Source Firkin
Remixed from a JPG that was uploaded to Pixabay by Osckar
Source Firkin
This is the remix of "Background pattern 115" uploaded by "Firkin".Thanks.
Source Yamachem
A free background image with a seamless texture of cardboard. This texture of cardboard looks quite realistic, especially when is actually tiled.
Source V. Hartikainen
From a design found in 'History of the Virginia Company of London; with letters to and from the first Colony, never before printed', Edward Neill, 1869.
Source Firkin
A seamless web texture with illustration of pale color stains on canvas.
Source V. Hartikainen
It has waves, so make sure you don’t get sea sickness.
Source CoolPatterns
The tile this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i
Source Firkin
Old China with a modern twist, take two.
Source Adam Charlts
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
An orange vertically striped background pattern. Feel free to download and use this orange background pattern, for example, on the web). It resembles a wallpaper with vertical stripes or something similar to it.
Source V. Hartikainen
Design drawn in Paint.net, vectorised using Vector Magic and finished in Inkscape.
Source Firkin
This was submitted in a beige color, hence the name. Now it’s a gray paper pattern.
Source Konstantin Ivanov
Sometimes simple really is what you need, and this could fit you well.
Source Factorio.us Collective
Classic 45-degree pattern, light version.
Source Luke McDonald
Simple wide squares with a small indent. Fits all.
Source Petr Šulc.
From a tile that can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
A simple but elegant classic. Every collection needs one of these.
Source Christopher Burton