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
Use shift+alt+i on the selected rectangle in Inkscape to get the tile this is based on
Source Firkin
Utilising some flowers from Almeidah. To get the unit tile, select the rectangle in Inkscape and use shift-alt-i.
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
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
Did anyone say The Hoff? This pattern is in no way related to Baywatch.
Source Josh Green
I know there is one here already, but this is sexy!
Source Gjermund Gustavsen
To get the tile this is based on, select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
Remixed from a design seen in 'Burghley. The Life of William Cecil', William Charlton, 1857
Source Firkin
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
Remixed from a drawing in 'Line and form', Walter Crane, 1914.
Source Firkin
Number five from the same submitter, makes my job easy.
Source Dima Shiper
Used in small doses, this could be a nice subtle pattern. Used on a large surface, it’s dirty!
Source Paul Reulat
The tile for this is based on a repeating unit close to a design on Pixabay. It can be had by selecting the rectangle in Inkscape and using shift-alt-i.
Source Firkin
Clean and crisp lines all over the place. Wrap it up with this one.
Source Dax Kieran
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
Pattern #100! A black classic knit-looking pattern.
Source Factorio.us Collective
This one looks like a cork panel. Feel free to use it as a tiled background on your blog or website.
Source V. Hartikainen
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
From a drawing in 'Les Chroniqueurs de l'Histoire de France depuis les origines jusqu'au XVIe siècle', Henriette Witt, 1884.
Source Firkin
Real snow that tiles, not easy. This is not perfect, but an attempt.
Source Atle Mo
This is the remix of an Openclipart clipart called "Maze" uploaded by "any_ono_mous".Thanks.This is a seamless pattern of a maze.
Source Yamachem