The starting point for this was a texture drawn with the 'Radial Colors' plug-in in Paint.net.
Source Firkin
From a drawing in 'Line and form', Walter Crane, 1914.
Source Firkin
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
Prismatic Geometric Pattern Background 2 No Black
Source GDJ
To get the tile this is based on, select the rectangle in Inkscape and use 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
Black brick wall pattern. Brick your site up!
Source Alex Parker
It has waves, so make sure you don’t get sea sickness.
Source CoolPatterns
Remixed from a drawing in 'Maidenhood; or, the Verge of the Stream', Laura Jewry, 1876.
Source Firkin
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
Tiny little fibers making a soft and sweet look.
Source Badhon Ebrahim
Retro Circles Background 8 No Black
Source GDJ
This makes me wanna shoot some pool! Sweet green pool table pattern.
Source Caveman
A background tile of dark textile. Made this a long time ago and just now decided to publish it.
Source V. Hartikainen
There are quite a few grid patterns, but this one is a super tiny grid with some dust for good measure.
Source Dominik Kiss
A seamless pale yellow paper background with a pattern of animal tracks.
Source V. Hartikainen
Prepared mostly as a raster in Paint.net and vectorised.
Source Firkin
This seamless background image should look nice on websites. It has a dark blue gray texture with vertical stripes, it tiles seamlessly and, like all of the background images here, it's free. So, if you like it, take it!
Source V. Hartikainen
This tiled background comes in red and consists of tiles that look like gemstones. It is more for blogs or social profiles, I think.
Source V. Hartikainen
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
Seamless pattern formed from a tile that can be had by selecting the rectangle in Inkscape 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
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