Here's a bluish gray striped background pattern for use on web sites.
Source V. Hartikainen
I skipped number 3, because it wasn’t all that great. Sorry.
Source Dima Shiper
A seamless pattern formed from a sports car on clker.com. To get the tile, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Prismatic Groovy Concentric Background 5
Source GDJ
Prismatic Curved Diamond Pattern 4 No Background
Source GDJ
Number 3 in a series of 5 beautiful patterns. Can be found in colors on the submitter’s website.
Source Janos Koos
Prismatic Rounded Squares Grid 3 No Background
Source GDJ
To get the tile this is formed from select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Prismatic Abstract Geometric Background 2 No Black
Source GDJ
Everyone needs some stardust. Sprinkle it on your next project.
Source Atle Mo
A bit simplified version. Although it could be edited out to be simpler. Anyway, this time the tiling is converted to a pattern fill -which is using clipping for the tile's edges.
Source Lazur URH
A lot of people like the icon patterns, so here’s one for your restaurant blog.
Source Andrijana Jarnjak
From a drawing in 'Studies for Stories', Jean Ingelow, 1864.
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
Prismatic Abstract Geometric Background 4
Source GDJ
An emulated “transparent” background pattern, like that of all kinds of computer graphics software.
Source AdamStanislav
This is a seamless pattern of regular hexagon which has a honeycomb structure.
Source Yamachem
Zero CC tileable brick texture, photographed and made by me. CC0
Source Sojan Janso
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
Made by distorting a simple pattern using the 'sin waves' plugin for Paint.net and vectorising in Vector Magic
Source Firkin
Formed by heavily distorting part of a an image of a fish uploaded to Pixabay by GLady
Source Firkin
Zero CC tillable hard cover red book with X shape marks. Scanned and made by me.
Source Sojan Janso