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
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
From a drawing in 'Sun Pictures of the Norfolk Broads', Ernest Suffling, 1892.
Source Firkin
The rectangular tile this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i
Source Firkin
Medium gray pattern with small strokes to give a weave effect.
Source Catherine
Because I love dark patterns, here is Brushed Alum in a dark coating.
Source Tim Ward
Prismatic Abstract Background Design
Source GDJ
From a drawing in 'Studies for Stories', Jean Ingelow, 1864.
Source Firkin
The image depicts a seamless pattern which includes hexagonally-aligned gourds with BG in light-brown.
Source Yamachem
On a large canvas you can see it tiling, but used on smaller areas, it’s beautiful.
Source Paul Phönixweiß
High detail stone wall with minor cracks and specks.
Source Projecteightyfive
Inspired by a pattern seen on a public domain image of a very old tile. To get the unit cell, select the rectangle in Inkscape and use 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
Tiny circle waves, almost like the ocean.
Source Sagive
This background pattern has futuristic look. So, maybe it could be used on websites or blogs dedicated to video games?!
Source V. Hartikainen
Just to prove my point, here is a slightly modified dark version.
Source Atle Mo
The image depicts polka dot seamless pattern.
Source Yamachem
Classic vertical lines, in all its subtlety.
Source Cody L
I love these crisp, tiny, super subtle patterns.
Source Badhon Ebrahim
Seamless Prismatic Pythagorean Line Art Pattern No Background. A seamless pattern that includes the original tile (go to Objects / Pattern / Pattern To Objects in Inkscape's menu to extract it).
Source GDJ
A repeating background of beige (or is it more vanilla yellow) textured stripes. One more background with stripes.
Source V. Hartikainen
Remixed from a raster on Pixabay that was uploaded by ArtsyBee.
Source Firkin
From a drawing in 'Art Embroidery', M.S. Lockwood and E. Glaister, 1878.
Source Firkin