Inspired by a pattern seen on a public domain image of a very old tile. To get the unit cell, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
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 nice and simple gray stucco material. Great on its own, or as a base for a new pattern.
Source Bartosz Kaszubowski
A free light orange brown wallpaper with vertical stripes designed for use as a tiled background on websites. An yet another background pattern with vertical stripes.
Source V. Hartikainen
One can never have too few rice paper patterns, so here is one more.
Source Atle Mo
Remixed from a drawing in 'Sun Pictures of the Norfolk Broads', Ernest Suffling, 1892.
Source Firkin
The image is a design of blue glass.How about using it as background image?
Source Yamachem
Prismatic Snowflakes Pattern 3 No Background
Source GDJ
Seamless , tileable CC-0 texture. Created by my own, feel free to use wherever you want!
Source Linolafett
A playful triangle pattern with different shades of gray.
Source Dimitrie Hoekstra
Derived from an image that was uploaded to Pixabay by TheDigitalArtist
Source Firkin