Black & white version of a pattern that came out of playing with the 'light rays' plug-in for Paint.net
Source Firkin
Seamless , tileable CC-0 texture. Created by my own, feel free to use wherever you want!
Source Linolafett
Dark, crisp and subtle. Tiny black lines on top of some noise.
Source Wilmotte Bastien
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
Prismatic Polka Dots Mark II No Background
Source GDJ
An abstract texture of black metal pipes (seamless).
Source V. Hartikainen
A seamless pattern recreated from an image on Pixabay. It is reminiscent of parquet flooring and is formed from a square tile, which can be recovered in Inkscape by selecting the ungrouped rectangle and using shift-alt-I together.
Source Firkin
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
From a drawing in 'Artists and Arabs', Henry Blackburn, 1868.
Source Firkin
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
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
This was formed by distorting an image of a background on Pixabay.
Source Firkin
The image depicts a Japanese Edo pattern called "kanoko or 鹿の子" meaning "fawn" which has a fur with small white spots.
Source Yamachem
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
To get the tile this is based on select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Not a flat you live inside, like in the UK – but a flat piece of cardboard.
Source Appleshadow
A blue gray fabric-like texture for websites. An yet another fabric-like texture. It has subtle vertical and diagonal stripes to it.
Source V. Hartikainen
And some more testing, this time with Seamless Studio. It’s Robots FFS!
Source Seamless Studio
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
A pattern formed from a squared tile. The tile can be accessed in Inkscape by selecting the rectangle and using shift-alt-i.
Source Firkin
Remixed from a drawing in 'Works. Popular edition', John Ruskin, 1886.
Source Firkin
Not strictly seamless in that opposite edges are not identical. But they do marry up to make an interesting pattern
Source Firkin
The tile can be had by using shift+alt+i on the selected rectangle in Inkscape
Source Firkin
This was formed by distorting an image of a background on Pixabay.
Source Firkin
The following repeating website background is colored in a blue gray color and resembles a concrete wall or something similar to it.
Source V. Hartikainen