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
Remixed from a PNG that was uploaded to Pixabay by k_jprather
Source Firkin
Prismatic Basic 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
Prismatic Abstract Geometric Background 2 No Black
Source GDJ
A seamless pattern based on a square tile that can be retrieved in Inkscape by selecting the rectangle and using shift-alt-i.
Source Firkin
From a drawing in 'Storia del Palazzo Vecchio in Firenze', Aurelio Gotti, 1889.
Source Firkin
No idea what Nistri means, but it’s a crisp little pattern nonetheless.
Source Markus Reiter
You may use it as is, or modify it as you like.
Source V. Hartikainen
Spice up your next school project with this icon background.
Source Swetha
Tiny little fibers making a soft and sweet look.
Source Badhon Ebrahim
Dark wooden pattern, given the subtle treatment. based on texture from Cloaks.
Remixed from a design seen on Pixabay. The basic tile can be had by selecting the rectangle in Inkscape and using shift+alt+i
Source Firkin
Remixed from a drawing in 'Works. Popular edition', John Ruskin, 1886.
Source Firkin
Prismatic Abstract Background Design
Source GDJ
Remixed from a drawing in 'Analecta Eboracensia', Thomas Widdrington, 1897.
Source Firkin
A colourful background drawn originally in paint.net and vectorised in Vector Magic.
Source Firkin
Remixed from a design on Pixabay. To get the tile this is based on select the rectangle in Inkscape and use shift-alt-i
Source Firkin
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
Background Wall, Art Abstract, Blue Well & CC0 texture.
Source Ractapopulous
Here's a new background image for websites with a seamless pink texture. It should look beautiful with website themes where light pink background is needed. The background is seamless, therefore it should be used as a tiled background.
Source V. Hartikainen
A nice one indeed, but I have a feeling we have it already? If you spot a copy, let me know on Twitter.
Source Graphiste
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
This is a more minute version of "fishnet 01".The image depicts a seamless pattern of a fishnet with a plenty of fish.It may be a lucky charm for fishermen.
Source Yamachem
Seamless , tileable CC-0 texture. Created by my own, feel free to use wherever you want!
Source Linolafett
Prismatic Curved Diamond Pattern 5 No Background
Source GDJ