A heavy hitter at 400x400px, but lovely still.
Source Breezi
Seamless pattern formed from a tile that can be had by selecting the rectangle in Inkscape and using shift-alt-i.
Source Firkin
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
This could be a hippy vintage wallpaper.
Source Tileable Patterns
From a drawing in 'Gately's World's Progress', Charles Beale, 1886.
Source Firkin
This one could be the shirt of a golf player. Angled lines in different thicknesses.
Source Olivier Pineda
The tile this is formed from can be retrieved in Inkscape by selecting the rectangle and using shift+alt+i
Source Firkin
Remixed from a design seen in 'Burghley. The Life of William Cecil', William Charlton, 1857.
Source Firkin
With a name this awesome, how can I go wrong?
Source Nikolay Boltachev
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
This pack of filters can help you adding a blocky overlay to objects. May come handy at drawing blocks of stone.
Source Lazur URH
Prismatic Groovy Concentric Background 2 No Black
Source GDJ
A seamless pattern the unit cell for which can be had by selecting the rectangle in Inkscape and using shift+alt+i
Source Firkin
Derived from a drawing in 'The Murmur of the Shells', Samuel Cowen, 1879.
Source Firkin
A seamless pattern the starting point for which was a 'rainbow twist' texture in Paint.net.
Source Firkin
From a drawing in 'In an Enchanted Island', William Mallock, 1892.
Source Firkin
The name is totally random, but hey, it sounds good.
Source Atle Mo
To get the tile this is based on select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
This one looks like a cork panel. Feel free to use it as a tiled background on your blog or website.
Source V. Hartikainen
Prismatic Groovy Concentric Background No Black
Source GDJ