Here's a bluish gray striped background pattern for use on web sites.
Source V. Hartikainen
You can never get enough of these tiny pixel patterns with sharp lines.
Source Designova
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
Light and tiny, just the way you like it.
Source Rohit Arun Rao
Alternative colour scheme. 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
From a drawing in 'Art Embroidery', M.S. Lockwood and E. Glaister, 1878.
Source Firkin
Formed from a tile based on a drawing from 'Viaggi d'un artista nell'America Meridionale', Guido Boggiani, 1895.
Source Firkin
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
Tiny little fibers making a soft and sweet look.
Source Badhon Ebrahim
Remixed from a drawing that was uploaded to Pixabay by ractapopulous
Source Firkin
This reminds me of Game Cube. A nice light 3D cube pattern.
Source Sander Ottens
A rusty grunge background for websites. Feel free to use it in your site's theme.
Source V. Hartikainen
From a drawing in 'Art Embroidery', M.S. Lockwood and E. Glaister, 1878.
Source Firkin
Someone was asking about how to achieve a fur pattern at #inkscape irc so tried to make a filter on it. Flood filled fractal noises rigged together. May someone find a good use for these.
Source Lazur URH
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
A background tile of dark textile. Made this a long time ago and just now decided to publish it.
Source V. Hartikainen
Sweet and subtle white plaster with hints of noise and grunge.
Source Phil Maurer
Colour version of the original pattern inspired by the front cover of 'Old and New Paris', Henry Edwards, 1894.
Source Firkin
A seamless design of flowers remixed from a jpg on Pixabay by Prawny.
Source Firkin
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
The tile this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i
Source Firkin
Square design drawn in Paint.net and vectorized in Vector Magic.
Source Firkin
Lovely pattern with some good-looking non-random noise lines.
Source Zucx