Submitted as a black pattern, I made it light and a few steps more subtle.
Source Andy
White little knobs, coming in at 10x10px. Sweet!
Source Amos
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
The name alone is awesome, but so is this sweet dark pattern.
Source Federica Pelzel
Seamless pattern formed from a tile that can be had by selecting the rectangle in Inkscape and using shift-alt-i.
Source Firkin
Not a pattern for fabrics, but one produced from a jpg of a stack of fabric items that was posted on Pixabay. The tile that this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
Seamless Green Tile Background
Source V. Hartikainen
The image a seamless pattern derived from a weed which I can't identify.The original weed image is from here:https://jp.pinterest.com/pin/500744052301423641/
Source Yamachem
It’s a hole, in a pattern. On your website. Dig it!
Source Josh Green
After 1 comes 2, same but different. You get the idea.
Source Hendrik Lammers
From a tile that can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
Prismatic Curved Diamond Pattern 2 No Background
Source GDJ
A seamless pattern based on a square tile that can be retrieved in Inkscape by selecting the rectangle and using shift-alt-i.
Source Firkin