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
Submitted in a cream color, but you know how I like it.
Source Devin Holmes
The basic shapes never get old. Simple triangle pattern.
Source Atle Mo
Nice little grid. Would work great as a base on top of some other patterns.
Source Arno Gregorian
Not even 1kb, but very stylish. Gray thin lines.
Source Struck Axiom
Black brick wall pattern. Brick your site up!
Source Alex Parker
Abstract Arbitrary Geometric Background derived from an image on Pixabay.
Source GDJ
Black & white version of a pattern that came out of playing with the 'light rays' plug-in for Paint.net
Source Firkin
Background Wall, Art Abstract, Blue Well & CC0 texture.
Source Ractapopulous
A large (588x375px) sand-colored pattern for your ever-growing collection. Shrink at will.
Source Alex Tapein
Sometimes simple really is what you need, and this could fit you well.
Source Factorio.us Collective
From a drawing in 'Art Embroidery', M.S. Lockwood and E. Glaister, 1878.
Source Firkin
Continuing the geometric trend, here is one more.
Source Mike Warner
A seamless pattern the starting point for which was a 'colour modulo' texture in Paint.net.
Source Firkin
This one has rusty dark brown texture.
Source V. Hartikainen
Prismatic Groovy Concentric Background 2 No Black
Source GDJ
A seamless pattern created from a square tile. To get the tile, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
One can never have too few rice paper patterns, so here is one more.
Source Atle Mo
A playful triangle pattern with different shades of gray.
Source Dimitrie Hoekstra
A lovely light gray pattern with stripes and a dash of noise.
Source V. Hartikainen
A simple but elegant classic. Every collection needs one of these.
Source Christopher Burton
Imagine you zoomed in 1000X on some fabric. But then it turned out to be a skeleton!
Source Angelica
I love cream! 50x50px and lovely in all the good ways.
Source Thomas Myrman
A bit strange this one, but nice at the same time.
Source Diogo Silva
An emulated “transparent” background pattern, like that of all kinds of computer graphics software.
Source AdamStanislav