Remixed from an image that was uploaded to Pixabay by Pixeline
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
Used a cherry by doctormo to make this seamless pattern
Source Firkin
The image is a seamless pattern of a fishnet.
Source Yamachem
A bit like some carbon, or knitted netting if you will.
Source Anna Litvinuk
Prismatic Groovy Concentric Background 3
Source GDJ
Non-seamless pattern drawn in Paint.net and vectorised in Vector Magic.
Source Firkin
This was formed by distorting an image of a background on Pixabay.
Source Firkin
The tile this is based on can be retrieved by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
Remixed from a JPG that was uploaded to Pixabay by theasad121
Source Firkin
If you like it a bit trippy, this wave pattern might be for you.
Source Ian Soper
Derived from a corner decoration itself found as a jpg on Pixabay.
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
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
Prismatic Basic Pattern 2 No Background
Source GDJ
The unit cell for this seamless pattern can be had in Inkscape by selecting the rectangle and using shift+alt+i.
Source Firkin
Design drawn in Paint.net, vectorised using Vector Magic and finished in Inkscape.
Source Firkin
This is a hot one. Small, sharp and unique.
Source GraphicsWall
A background pattern with a look of rough fabric.
Source V. Hartikainen
Prismatic Abstract Geometric Background 4 No Black
Source GDJ
Remixed from a drawing in 'Paul's Sister', Frances Peard, 1889.
Source Firkin
Like the name suggests, this background image consists of a pattern of dark bricks. It may be an option for you, if you are looking for something that looks like a brick wall for use as a background on web pages. It's not a masterpiece, but looks pretty nice when is tiled.
Source V. Hartikainen