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
To get the tile this is formed from select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
A smooth mid-tone gray, or low contrast if you will, linen pattern.
Source Jordan Pittman
A seamless pattern created from a square tile. To get the tile, select the pattern in Inkscape and use shift+alt+i.
Source Firkin
This is the remix of "polka dot seamless pattern".The image depicts polka dot seamless pattern.
Source Yamachem
The image is a remix of "edo pattern-samekomon".I changed the color of dots from black to white and added BG in light-yellow.
Source Yamachem
If you’re sick of the fancy 3D, grunge and noisy patterns, take a look at this flat 2D brick wall.
Source Listvetra
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
A seamless pattern formed from cross 4. To get the original tile select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
Actually remixed from a pattern on Pixabay. But then noticed a very similar one on Openclipart.org uploaded by btj51q2.
Source Firkin
From a design found in 'History of the Virginia Company of London; with letters to and from the first Colony, never before printed', Edward Neill, 1869.
Source Firkin
Dark, lines, noise, tactile. You get the drift.
Source Anatoli Nicolae
A seamless pattern formed from a square tile. The tile can be retrieved by selecting the rectangle in Inkscape and using shift-alt-i.
Source Firkin
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
Inspired by a drawing seen in 'City of Liverpool', James Picton, 1883.
Source Firkin
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
It’s like Shine Dotted’s sister, only rotated 45 degrees.
Source mediumidee
This was formed by distorting an image of a background on Pixabay.
Source Firkin
The first pattern on here using opacity. Try it on a site with a colored background, or even using mixed colors.
Source Nathan Spady
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
Derived from elements found in a floral ornament drawing on Pixabay.
Source Firkin
From a drawing in 'Les Chroniqueurs de l'Histoire de France depuis les origines jusqu'au XVIe siècle', Henriette Witt, 1884.
Source Firkin