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
Prismatic Geometric Tessellation Pattern 2 No Background
Source GDJ
From a drawing in 'Art Embroidery', M.S. Lockwood and E. Glaister, 1878.
Source Firkin
From a drawing in 'Studies for Stories', Jean Ingelow, 1864.
Source Firkin
From a drawing in 'Art Embroidery', M.S. Lockwood and E. Glaister, 1878.
Source Firkin
A seamless pattern drawn originally in Paint.net by distorting a slice of background pattern 116 and copying the resulting triangle numerous times.
Source Firkin
Classic vertical lines, in all its subtlety.
Source Cody L
Prismatic Hexagonalism Pattern No Background
Source GDJ
Light gray grunge wall with a nice texture overlay.
Source Adam Anlauf
This seamless pattern consists of a blue grid on a yellow background.
Source V. Hartikainen
A seamless background pattern of dark brown wood planks.
Source V. Hartikainen
An alternative colour scheme for the original seamless texture formed from an image on Pixabay.
Source Firkin
From a tile that can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
Classy golf-pants pattern, or crossed stripes if you will.
Source Will Monson
To get the tile this is based on, select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
Scanned some rice paper and tiled it up for you. Enjoy.
Source Atle Mo
Here is a new seamless wood texture for using as blog or website backgrounds.
Source V. Hartikainen
Classic vertical lines, in all its subtlety.
Source Cody L
A very dark asfalt pattern based off of a photo taken with my iPhone.
Source Atle Mo
Prismatic Geometric Tessellation Pattern 3 No Background
Source GDJ
A seamless pattern formed from cross 4. To get the original tile select the rectangle in Inkscape and use shift-alt-i.
Source Firkin