Sharp but soft triangles in light shades of gray.
Source Pixeden
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
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
The tile this is based on was adapted from an image that was uploaded to Pixabay by frolicsomepl. It can be had in Inkscape by selecting the rectangle and using shift+alt+i
Source Firkin
Prismatic Geometric Pattern Background
Source GDJ
The image depicts a seamless pattern of a tortoise in tortoiseshell (hexagon).
Source Yamachem
Prismatic Snowflakes Pattern 2 No Background
Source GDJ
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
Dead simple but beautiful horizontal line pattern.
Source Fabian Schultz
A seamless pattern the unit cell for which can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
Seamless Dark Grunge Texture. Here's a new grunge texture for use as a background.
Source V. Hartikainen
Same as the black version, but now in shades of gray. Very subtle and fine grained.
Source Atle Mo
A seamless chequerboard pattern formed from a tile that can be had in Inkscape by selecting the rectangle and using shift+alt+i. Alternative colour scheme.
Source Firkin
Adapted heavily from a JPG that was uploaded to Pixabay by Viscious-Speed.
Source Firkin
If you want png files of this u can download them here : viscious-speed.deviantart.com/gallery/27635117
Source Viscious-Speed
A seamless pattern from a tile drawn in Paint.net and vectorised in Vector Magic
Source Firkin
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
The tile can be had by selecting the rectangle in Inkscape and using shift+alt+i. Remixed from a drawing in 'Flowers of Song', Frederick Weatherly, 1895.
Source Firkin
An abstract pale yellow paper-like background with stains colored in yellow and green.
Source V. Hartikainen
Inspired by a pattern seen on a public domain image of a very old tile. To get the unit cell, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Nice and simple crossed lines in dark gray tones.
Source Stefan Aleksić
You could get a bit dizzy from this one, but it might come in handy.
Source Dertig Media
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i
Source Firkin
Prismatic Geometric Pattern Variation 2 With Background
Source GDJ