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
Scanned some rice paper and tiled it up for you. Enjoy.
Source Atle Mo
From an image on opengameart.org shared by rubberduck.
Source Firkin
The unit cell for this seamless pattern can be had in Inkscape by selecting the rectangle and using shift+alt+i.
Source Firkin
A dark striped seamless pattern suitable for use as a background on websites.
Source V. Hartikainen
To get the tile this is based on select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
From a drawing in 'Navigations de Alouys de Cademoste.-La Navigation du Capitaine Pierre Sintre', Alvise da ca da Mosto, 1895.
Source Firkin
This is indeed a bit strange, but here’s to the crazy ones!
Source Christopher Buecheler
A seamless texture of worn out "cardboard".
Source V. Hartikainen
A subtle shadowed checkered pattern. Increase the lightness for even more subtle sexiness.
Source Josh Green
Just the symbols of the signs of the zodiac distributed in a chequer board-like pattern
Source Firkin
It was called Navy Blue, but I made it dark. You know, the way I like it.
Source Ethan Hamilton
This ons is quite old school looking. Retro, even. I like it.
Source Arno Declercq
This was formed by distorting an image of a background on Pixabay.
Source Firkin
Plywood Web Background background image for use in web design.
Source V. Hartikainen
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
Dark and hard, just the way we like it. Embossed triangles makes a nice pattern.
Source Ivan Ginev
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
Imagine you zoomed in 1000X on some fabric. But then it turned out to be a skeleton!
Source Angelica
From a drawing in 'Art Embroidery', M.S. Lockwood and E. Glaister, 1878.
Source Firkin
Remixed from a drawing in 'Maidenhood; or, the Verge of the Stream', Laura Jewry, 1876.
Source Firkin