Submitted as a black pattern, I made it light and a few steps more subtle.
Source Andy
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
Prismatic Curved Diamond Pattern No Background
Source GDJ
A very slick dark rubber grip pattern, sort of like the grip on a camera.
Source Sinisha
In the spirit of WWDC 2011, here is a dark iOS inspired linen pattern.
Source Atle Mo
Orange-red pattern for tiled backgrounds.
Source V. Hartikainen
Inspired by a pattern found in 'Sun Pictures of the Norfolk Broads', Ernest Suffling, 1892.
Source Firkin
Prismatic Hypnotic Pattern No Background
Source GDJ
Inspired by a JPG that was uploaded to Pixabay by kokon_art
Source Firkin
Prismatic Triangular Background Design Mark II 5
Source GDJ
The image depicts meshed silhouettes of various things.The original image is an OCAL clipart called "Enter FOSSASIA 2016 #IoT T-shirt Design Contest" uploaded by "openclipart".Thanks.
Source Yamachem
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
Nothing like a clean set of bed sheets, huh?
Source Badhon Ebrahim
A seamless background pattern of dark brown wood planks.
Source V. Hartikainen
From a drawing in 'Royal Ramsgate', James Simson, 1897.
Source Firkin
The unit cell for this seamless pattern can be had in Inkscape by selecting the rectangle and using shift+alt+i
Source Firkin
To get the tile this is based on select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
White fabric looking texture with some nice random wave features.
Source Hendrik Lammers
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
This is so subtle: We’re talking 1% opacity. Get your squint on!
Source Atle Mo