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
From a drawing in 'The Quiver of Love', Walter Crane, 1876
Source Firkin
Prismatic Groovy Concentric Background No Black
Source GDJ
To get the tile this is based on select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Zero CC tileable hard cover green book, scanned and made by me. CC0
Source Sojan Janso
From a drawing in 'Prose and Verse ', William Linton, 1836.
Source Firkin
To get the tile this is based on, select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
CC0 and seamless wellington boot pattern.
Source SliverKnight
A seamless pattern drawn originally in Paint.net by distorting a slice of background pattern 116 and copying the resulting triangle numerous times.
Source Firkin
Original minus the background
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
Drawn in Paint.net and vectorised in Vector Magic.
Source Firkin
A version without colours blended together to give a different look.
Source Firkin
Vector version of a png that was uploaded to Pixabay by pencilparker
Source Firkin
A nice one indeed, but I have a feeling we have it already? If you spot a copy, let me know on Twitter.
Source Graphiste
A free seamless background image with a texture of dark red "canvas". It should look very nice on web sites.
Source V. Hartikainen
After 1 comes 2, same but different. You get the idea.
Source Hendrik Lammers
Seamless pattern formed from a tile that can be had by selecting the rectangle in Inkscape and using shift+alt+i
Source Firkin
A seamless pattern that includes the original tile (go to Objects / Pattern / Pattern To Objects in Inkscape's menu to extract it).
Source GDJ
Formed by heavily distorting part of a an image of a fish uploaded to Pixabay by GLady
Source Firkin
From a drawing in 'At home', J. Sowerby, J. Crane and T. Frederick, 1881.
Source Firkin
Tiny, tiny 3D cubes. Reminds me of the good old pattern from k10k.
Source Etienne Rallion
This background pattern has futuristic look. So, maybe it could be used on websites or blogs dedicated to video games?!
Source V. Hartikainen
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
Not a pattern for fabrics, but one produced from a jpg of a stack of fabric items that was posted on Pixabay. The tile that this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
Brushed aluminum, in a bright gray version. Lovely 2X as well.
Source Andre Schouten