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
8 by 8 pixels, and just what the title says.
Source pixilated
A simple example on using clones. You can generate a nice base for a pattern fill quickly with it.
Source Lazur URH
A seamless pattern created from a square tile. To get the tile, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Formed by heavily distorting part of a an image of a fish uploaded to Pixabay by GLady
Source Firkin
Recreated from a pattern found in 'Az Osztrák-Magyar Monarchia irásban és képben', 1882. To get the tile this is based on select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Square design drawn in Paint.net and vectorized in Vector Magic.
Source Firkin
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
8 by 8 pixels, and just what the title says.
Source pixilated
Awesome name, great pattern. Who does not love space?
Source Nick Batchelor
Has nothing to do with toast, but it’s nice and subtle.
Source Pippin Lee
Dead simple but beautiful horizontal line pattern.
Source Fabian Schultz
A repeating background of thick textured paper. Actually, it turned out to look like something between a paper and fabric.
Source V. Hartikainen
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
You could get a bit dizzy from this one, but it might come in handy.
Source Dertig Media
From a drawing in 'Bond Slaves. The story of a struggle.', Isabella Varley, 1893.
Source Firkin
A monochrome pattern from a tile that can be had by selecting the rectangle in Inkscaope and using shift+alt+i
Source Firkin
On a large canvas you can see it tiling, but used on smaller areas, it’s beautiful.
Source Paul Phönixweiß
A white version of the very popular linen pattern.
Source Ant Ekşiler
A seamless pattern from a tile made from a jpg on Pixabay. To get the tile select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
Feel free to download and use it, or see the rest of the dark background patterns that I have made. Anyway, I hope you will find something that you like.
Source V. Hartikainen
Remixed from a drawing in 'Line and form", Walter Crane, 1914.
Source Firkin
This texture looks like old leather. It should look great as a background on web pages.
Source V. Hartikainen
A monochrome pattern from a tile that can be had by selecting the rectangle in Inkscaope and using shift+alt+i
Source Firkin
Remixed from a drawing in 'Line and form', Walter Crane, 1914.
Source Firkin