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
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
As far as fabric patterns goes, this is quite crisp.
Source Heliodor Jalba
Because I love dark patterns, here is Brushed Alum in a dark coating.
Source Tim Ward
A seamless pattern the starting point for which was a 'colour modulo' texture in Paint.net.
Source Firkin
A pale olive green background with a seamless texture.
Source V. Hartikainen
Prismatic Abstract Line Art Pattern Background 2
Source GDJ
From a drawing in 'Maidenhood; or, the Verge of the Stream', Laura Jewry, 1876.
Source Firkin
Paper model of a tetrahedron. Modelo de papel de um tetraedro.
Source laobc
ZeroCC tileable moss texture, photographed and made by me. CC0
Source Sojan Janso
This is the remix of "polka dot seamless pattern".The image depicts polka dot seamless pattern.
Source Yamachem
This was formed by distorting an image of a background on Pixabay.
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
Remixed from a drawing in 'The March of Loyalty', Letitia MacClintock, 1884.
Source Firkin
Dark, square, clean and tidy. What more can you ask for?
Source Jaromír Kavan
Greyscale version of a pattern that came out of playing with the 'slinky' plug-in for Paint.net
Source Firkin
Very simple, very blu(e). Subtle and nice.
Source Seb Jachec
A seamless pattern made from the gold Penrose triangle by GDJ and the two remixes
Source Firkin
A very slick dark rubber grip pattern, sort of like the grip on a camera.
Source Sinisha
Wasn't satisfied with the original's colouring. Too much component transfer and colormatrixes yet the results are lacking a bit. So this time it is a simple black to transparent fade, making it possible remixing easily once there will be other blending modes supported as well. Probably in inkscape 0.92.
Source Lazur URH