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 Curved Diamond Pattern 2 No Background
Source GDJ
This is the remix of an OCAL clipart called "Art Nouveau ornament" uploaded by "microcosme".Thanks.This is a seamless pattern of an Art Nouveau ornament.
Source Yamachem
The image depicts a shell seamless pattern.I used an OCAL clipart called "Shell" uploaded by "jgm104".Thanks.
Source Yamachem
Super subtle indeed, a medium gray pattern with tiny dots in a grid.
Source Designova
Made by distorting a simple pattern using the 'sin waves' plugin for Paint.net and vectorising in Vector Magic
Source Firkin
As far as fabric patterns goes, this is quite crisp.
Source Heliodor Jalba
This is the remix of "polka dot seamless pattern".The image depicts polka dot seamless pattern.
Source Yamachem
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
Fix and cc0 to get the tile this is based on.
Source SliverKnight
Dark squares with some virus-looking dots in the grid.
Source Hugo Loning
Simple combination of stripy squares with their negatively coloured counterparts
Source Firkin
Remixed from a drawing in 'An Index to Deering's Nottinghamia Vetus et Nova', Rupert Chicken, 1899. The unit tile can be had by selecting the rectangle in Inkscape and using shift-alt-i
Source Firkin
This one could be the shirt of a golf player. Angled lines in different thicknesses.
Source Olivier Pineda
Small gradient crosses inside 45-degree boxes, or bigger crosses if you will.
Source Wassim
We have some linen patterns here, but none that are stressed. Until now.
Source Jordan Pittman
No, not the band but the pattern. Simple squares in gray tones, of course.
Source Atle Mo
A heavy hitter at 400x400px, but lovely still.
Source Breezi
This was formed by distorting an image of a background on Pixabay.
Source Firkin
A nice looking light gray background pattern with diagonal stripes.
Source V. Hartikainen
Alternative colour scheme for the original floral pattern.
Source Firkin
If you want png files of this u can download them here : viscious-speed.deviantart.com/gallery/27635117
Source Viscious-Speed
Zero CC tileable seed texture, edited by me to be seamless from a Pixabay image. CC0
Source Sojan Janso