Nice little grid. Would work great as a base on top of some other patterns.
Source Arno Gregorian
Prismatic Curved Diamond Pattern 8 No Background
Source GDJ
No relation to the band, but damn it’s subtle!
Source Thomas Myrman
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
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
From a drawing in 'Cassell's Library of English Literature', Henry Morley, 1883.
Source Firkin
Drawn in Paint.net using the kaleidoscope plug-in and vectorised.
Source Firkin
Black And White Floral Pattern Background from PDP.
Source GDJ
Made by distorting a simple pattern using the 'sin waves' plugin for Paint.net and vectorising in Vector Magic
Source Firkin
One can never have too few rice paper patterns, so here is one more.
Source Atle Mo
Turn your site into a dragon with this great scale pattern.
Source Alex Parker
Not even 1kb, but very stylish. Gray thin lines.
Source Struck Axiom
A version without colours blended together to give a different look.
Source Firkin
Simple combination of stripy squares with their negatively coloured counterparts
Source Firkin
Prismatic Groovy Concentric Background 5
Source GDJ
I guess this one is inspired by an office. A dark office.
Source Andrés Rigo.
Light and tiny, just the way you like it.
Source Rohit Arun Rao
Heavy depth and shadows here, but might work well on some mobile apps.
Source Damian Rivas
Derived from a drawing in 'Historiske Afhandlinger', Adolf Jorgensen, 1898.
Source Firkin
Sharp pixel pattern, just like the good old days.
Source Paridhi