Seamless pattern the tile for which can be had by using shift-alt-I on the selected rectangle in Inkscape.
Source Firkin
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
Just like your old suit, all striped and smooth.
Source Alex Berkowitz
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Remixed from an image that was uploaded to Pixabay by Pixeline
Source Firkin
More Japanese-inspired patterns, Gold Scales this time.
Source Josh Green
This tiled background comes in red and consists of tiles that look like gemstones. It is more for blogs or social profiles, I think.
Source V. Hartikainen
It’s like Shine Dotted’s sister, only rotated 45 degrees.
Source mediumidee
A fun-looking elastoplast/band-aid pattern. A hint of orange tone in this one.
Source Josh Green
Psychedelic Geometric Background No Black
Source GDJ
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
A beautiful dark wood pattern, superbly tiled.
Source Omar Alvarado
Pass parameters to the URL or edit the source code variables to configure the graph paper for the division desired.
Source JayNick
Remixed from a drawing in 'Maidenhood; or, the Verge of the Stream', Laura Jewry, 1876.
Source Firkin
This is so subtle I hope you can see it! Tweak at will.
Source Alexandre Naud
Prismatic Polka Dots Mark II 2 No Background
Source GDJ
Colour version of a pattern that came out of playing with the 'light rays' plug-in for Paint.net
Source Firkin
Prismatic Triangular Background Design Mark II 5
Source GDJ
Derived from elements found in a floral ornament drawing on Pixabay.
Source Firkin
Lovely light gray floral motif with some subtle shades.
Source GraphicsWall
Pattern formed from simple shapes. Black version.
Source Firkin
The green fibers pattern will work very well in grayscale as well.
Source Matteo Di Capua
Seamless , tileable CC-0 texture. Created by my own, feel free to use wherever you want!
Source Linolafett
A simple bump filter made upon request at irc #inkscape at freenode. Made a screen capture of the making here: https://youtu.be/TGAWYKVLxQw
Source Lazur URH