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
Sometimes simple really is what you need, and this could fit you well.
Source Factorio.us Collective
A white version of the very popular linen pattern.
Source Ant Ekşiler
To get the tile this is based on select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Because I love dark patterns, here is Brushed Alum in a dark coating.
Source Tim Ward
This reminds me of Game Cube. A nice light 3D cube pattern.
Source Sander Ottens
Number 2 in a series of 5 beautiful patterns. Can be found in colors on the submitter’s website.
Source Janos Koos
Nothing like a clean set of bed sheets, huh?
Source Badhon Ebrahim
A light gray fabric pattern with faded vertical stripes.
Source V. Hartikainen
Zero CC tileable seed texture, edited by me to be seamless from a Pixabay image. CC0
Source Sojan Janso
Geometric triangles seem to be quite hot these days.
Source Pixeden
Hey, you never know when you’ll need a bird pattern, right?
Source Pete Fecteau
Black paper texture, based on two different images.
Source Atle Mo
Based from Design Kindle
Remixed from a drawing in 'Line and form', Walter Crane, 1914.
Source Firkin
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
Brushed aluminum, in a bright gray version. Lovely 2X as well.
Source Andre Schouten
Zero CC tileable hard cover red book, scanned and made by me. CC0
Source Sojan Janso
U.S.-based National Fire Protection Association standard fire diamond for flagging risks posed by hazardous materials. The red diamond has a number 0-4 depending on flammability. The blue diamond has a number 0-4 depending on health hazard. The yellow has a number 0-4 depending on reactivity. the white square has a special notice, e.g OX for oxidizer.
Source Firkin
Light gray grunge wall with a nice texture overlay.
Source Adam Anlauf
A repeating background for websites with a texture of black groove stripes.
Source V. Hartikainen
Nice little grid. Would work great as a base on top of some other patterns.
Source Arno Gregorian
From a drawing in 'Line and form', Walter Crane, 1914.
Source Firkin
Sounds French. Some 3D square diagonals, that’s all you need to know.
Source Graphiste