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
One more sharp little tile for you. Subtle circles this time.
Source Blunia
Prismatic Snowflakes Pattern 2 No Background
Source GDJ
Clean and crisp lines all over the place. Wrap it up with this one.
Source Dax Kieran
Remixed from a drawing in 'Line and form', Walter Crane, 1914.
Source Firkin
A seamless chequerboard pattern formed from a tile that can be had in Inkscape by selecting the rectangle and using shift+alt+i. Alternative colour scheme.
Source Firkin
Hexagonal dark 3D pattern. What more can you ask for?
Source Norbert Levajsics
A very dark asfalt pattern based off of a photo taken with my iPhone.
Source Atle Mo
Prismatic Hypnotic Pattern 2 No Background
Source GDJ
Background Wall, Art Abstract, white Well & CC0 texture.
Source Ractapopulous
Remixed from a drawing in 'The March of Loyalty', Letitia MacClintock, 1884.
Source Firkin
This tiled background comes in red and consists of tiles that look like gemstones. It is more for blogs or social profiles, I think.
Source V. Hartikainen
Design drawn in Paint.net, vectorised using Vector Magic and finished in Inkscape.
Source Firkin
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
This background pattern looks like bamboo to me. Feel free to download it for your website (for your blog perhaps?).
Source V. Hartikainen
A seamless pattern the starting point for which was a 'light rays' rendering in Paint.net.
Source Firkin
The base gradient edited so now more details are rendered.
Source Lazur URH
Because I love dark patterns, here is Brushed Alum in a dark coating.
Source Tim Ward
A grid of squares with green colours. Since the colours are randomly distributed it is automatically seamless.
Source Firkin
Seamless pattern formed from a tile that can be had by selecting the rectangle in Inkscape and using shift-alt-i.
Source Firkin
An interesting dark spotted pattern at an angle.
Source Hendrik Lammers