Scanned some rice paper and tiled it up for you. Enjoy.
Source Atle Mo
Seamless , tileable CC-0 texture. Created by my own, feel free to use wherever you want!
Source Linolafett
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 pattern created from a square tile. To get the tile, select the pattern in Inkscape and use shift+alt+i.
Source Firkin
A gray background pattern with a texture of textile. Suits perfectly for web design.
Source V. Hartikainen
Light gray paper pattern with small traces of fiber and some dust.
Source Atle Mo
One more from Badhon, sharp horizontal lines making an embossed paper feeling.
Source Badhon Ebrahim
Clean and crisp lines all over the place. Wrap it up with this one.
Source Dax Kieran
From a drawing in 'Resa i Afrika, genom Angola, Ovampo och Damaraland', P. Moller, 1899.
Source Firkin
Derived from a corner decoration itself found as a jpg on Pixabay.
Source Firkin
Prepared mostly as a raster in Paint.net and vectorised.
Source Firkin
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
The image depicts a seamless pattern of pine tree leaves.
Source Yamachem
Remixed from a PNG that was uploaded to Pixabay by k_jprather
Source Firkin
Remixed from a drawing in 'Analecta Eboracensia', Thomas Widdrington, 1897.
Source Firkin
You were craving more leather, so I whipped this up by scanning a leather jacket.
Source Atle Mo
From a drawing in 'The Quiver of Love', Walter Crane, 1876
Source Firkin
The original enhanced with some gradients.
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
Sharp diamond pattern. A small 24x18px tile.
Source Tom Neal
Made by distorting a simple pattern using the 'sin waves' plugin for Paint.net and vectorising in Vector Magic
Source Firkin
Remixed from a drawing in 'Hungary. A guide book. By several authors', 1890.
Source Firkin
This background pattern contains a seamless texture of bark. It's not very realistic, but I think it looks quite nice.
Source V. Hartikainen
Seamless pattern the tile for which can be had by using shift-alt-I on the selected rectangle in Inkscape.
Source Firkin