I skipped number 3, because it wasn’t all that great. Sorry.
Source Dima Shiper
From a drawing in 'Art Embroidery', M.S. Lockwood and E. Glaister, 1878.
Source Firkin
A seamless pattern based on a rectangular tile that can be retrieved in Inkscape by selecting the rectangle and using shift-alt-i.
Source Firkin
Recreated from a pattern found in 'Az Osztrák-Magyar Monarchia irásban és képben', 1882. To get the tile this is based on select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Vector version of a png that was uploaded to Pixabay by pencilparker
Source Firkin
Turn your site into a dragon with this great scale pattern.
Source Alex Parker
If you like it a bit trippy, this wave pattern might be for you.
Source Ian Soper
Tiny circle waves, almost like the ocean.
Source Sagive
Alternative colour scheme. 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
A frame using leaves from an image that was uploaded to Pixabay by mayapujiati
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
An abstract texture of black metal pipes (seamless).
Source V. Hartikainen
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
With a name this awesome, how can I go wrong?
Source Nikolay Boltachev
Green Web Background, Seamless tile.
Source V. Hartikainen
Have you wondered about how it feels to be buried alive? Here is the pattern for it.
Source Hendrik Lammers
If you don’t like cream and pixels, you’re in the wrong place.
Source Mizanur Rahman
Here is a new seamless wood texture for using as blog or website backgrounds.
Source V. Hartikainen
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Sharp but soft triangles in light shades of gray.
Source Pixeden
From a drawing in 'Az Osztrák-Magyar Monarchia irásban és képben', 1885.
Source Firkin
The tile this fill pattern is based on can be had by using shift+alt+i on the rectangle.
Source Firkin
Oh yes, it happened! A pattern in full color.
Source Atle Mo
A large pattern with funky shapes and form. An original. Sort of origami-ish.
Source Luuk van Baars