The tile this is based on can be retrieved 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
Prismatic Abstract Line Art Pattern Background 2
Source GDJ
Remixed from a design on Pixabay. To get the tile this is based on select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
I have no idea what J Boo means by this name, but hey – it’s hot.
Source j Boo
Based on an image that was uploaded to Pixabay by devanath
Source Firkin
A heavy hitter at 400x400px, but lovely still.
Source Breezi
This is a remix of "blue wave-seigaiha".I hope this subtle color version of Seigaiha would be suitable for background .
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
This one takes you back to math class. Classic mathematic board underlay.
Source Josh Green
Derived from an image that was uploaded to Pixabay by Darkmoon1968
Source Firkin
A dark pattern made out of 3×3 circles and a 1px shadow. This works well as a carbon texture or background.
Source Atle Mo
Zero CC tileable moss or lichen covered stone texture, edited from pixabay. CC0
Source Sojan Janso