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 rectangle in Inkscape and use 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
More in the paper realm, this time with fibers.
Source Jorge Fuentes
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
There are many carbon patterns, but this one is tiny.
Source Designova
A seamless background drawn in Paint.net and vectorised with Vector Magic. The starting point was a photograph of drinking straws from Pixabay.
Source Firkin
Zero CC tileable grass texture, photographed and made by me. CC0
Source Sojan Janso
Carbon fiber is never out of fashion, so here is one more style for you.
Source Alfred Lee
"Beige Stone", Tileable Texture.
Source V. Hartikainen
Light gray version of the Binding pattern that looks a bit like fabric.
Source Newbury
Love me some light mesh on a Monday. Sharp.
Source Wilmotte Bastien
Vector version of a png that was uploaded to Pixabay by pencilparker
Source Firkin
Vector version of a png that was uploaded to Pixabay by pencilparker
Source Firkin
Remixed from a JPG that was uploaded to Pixabay by susanlu4esm
Source Firkin
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Prismatic Curved Diamond Pattern 3 No Background
Source GDJ
Remixed from a drawing in 'Очерки Русской Исторіи въ памятникахъ быта', Petr Polevoi, 1879.
Source Firkin
Tiny, tiny 3D cubes. Reminds me of the good old pattern from k10k.
Source Etienne Rallion
Sharp pixel pattern looking like some sort of fabric.
Source Dmitry
Formed from decorative divider 184 in paint.net. Vectorised with Vector Magic.
Source Firkin
U.S.-based National Fire Protection Association standard fire diamond for flagging risks posed by hazardous materials. The red diamond has a number 0-4 depending on flammability. The blue diamond has a number 0-4 depending on health hazard. The yellow has a number 0-4 depending on reactivity. the white square has a special notice, e.g OX for oxidizer.
Source Firkin