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
Remixed from a drawing in 'Analecta Eboracensia', Thomas Widdrington, 1897.
Source Firkin
Sometimes simple really is what you need, and this could fit you well.
Source Factorio.us Collective
From an image on opengameart.org shared by rubberduck.
Source Firkin
A background formed from an image of an old tile on the New York Metropolitan Museum of Art website. To get the base tile, select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
Prismatic Curved Diamond Pattern 5 No Background
Source GDJ
Light gray version of the Binding pattern that looks a bit like fabric.
Source Newbury
Remixed from a drawing in 'Hungary. A guide book. By several authors', 1890.
Source Firkin
This was formed by distorting an image of a background on Pixabay.
Source Firkin
A pattern drawn in Paint.net and vectorized in Inkscape.
Source Firkin
A background formed from an image of an old tile on the New York Metropolitan Museum of Art website. To get the base tile, select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
A slightly more textured pattern, medium gray. A bit like a potato sack?
Source Bilal Ketab
This ladies and gentlemen, is texturetastic! Love it.
Source Adam Pickering
Zero CC tileable wood texture, made by me procedurally in Neo Texture Edit.
Source Sojan Janso
Medium gray fabric pattern with 45-degree lines going across.
Source Atle Mo
Prismatic Groovy Concentric Background 4
Source GDJ
Prismatic Hypnotic Pattern 2 No Background
Source GDJ
A monochrome pattern from a tile that can be had by selecting the rectangle in Inkscaope and using shift+alt+i
Source Firkin
Kaleidoscope Prismatic Abstract No Background
Source GDJ
It’s like Shine Dotted’s sister, only rotated 45 degrees.
Source mediumidee
Prismatic Isometric Cube Wireframe Pattern No Background
Source GDJ
Prismatic Groovy Concentric Background 4 No Black
Source GDJ
From a drawing in 'Line and form', Walter Crane, 1914.
Source Firkin
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Seamless pattern the tile for which can be had by using shift-alt-I on the selected rectangle in Inkscape.
Source Firkin
A seamless pattern the starting point for which was a 'rainbow twist' texture in Paint.net.
Source Firkin
The tile this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i
Source Firkin
Not so subtle. These tileable wood patterns are very useful.
Source Elemis
Remixed from a drawing in 'Line and form", Walter Crane, 1914.
Source Firkin