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 is indeed a bit strange, but here’s to the crazy ones!
Source Christopher Buecheler
An interesting dark spotted pattern at an angle.
Source Hendrik Lammers
You were craving more leather, so I whipped this up by scanning a leather jacket.
Source Atle Mo
A seamless pattern formed from cross 4. To get the original tile select the rectangle in Inkscape and use 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
CC0 and a seamless pattern from a tile drawn in Paint.net .
Source SliverKnight
Fabric-ish patterns are close to my heart. French Stucco to the rescue.
Source Christopher Buecheler
A playful triangle pattern with different shades of gray.
Source Dimitrie Hoekstra
ZeroCC tileable mossy (lichen) stone texture, edited from pixabay. CC0
Source Sojan Janso
Prismatic Curved Diamond Pattern 3 No Background
Source GDJ
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
Derived from an image that was uploaded to Pixabay by Kaz
Source Firkin
Zero CC tileable yellow craft paper; scanned 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
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 Green Tile Background
Source V. Hartikainen
Orange-red pattern for tiled backgrounds.
Source V. Hartikainen
From a drawing in 'Art Embroidery', M.S. Lockwood and E. Glaister, 1878.
Source Firkin
If you like it a bit trippy, this wave pattern might be for you.
Source Ian Soper