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
Here's a new paper-like background for free use on personal and commercial projects (this applies to all background patterns here).
Source V. Hartikainen
A colourful background drawn originally in paint.net and vectorised in Vector Magic.
Source Firkin
A pattern derived from repeating unit cells each derived from part of a fractal rendering in paint.net.
Source Firkin
This is so subtle I hope you can see it! Tweak at will.
Source Alexandre Naud
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
From a drawing in 'Art Embroidery', M.S. Lockwood and E. Glaister, 1878.
Source Firkin
Prismatic Geometric Tessellation Pattern No Background
Source GDJ
This one is something special. I’d call it a flat pattern, too. Very well done, sir!
Source GetDiscount
Abstract Ellipses Background Grayscale
Source GDJ
I’m guessing this is related to the Sony Vaio? It’s a nice pattern no matter where it’s from.
Source Zigzain
Seamless Background For Websites. It has a texture similar to cork-board.
Source V. Hartikainen
White circles connecting on a light gray background.
Source Mark Collins
Derived from an image that was uploaded to Pixabay by mdmelo.
Source Firkin
Derived from an image that was uploaded to Pixabay by Kaz
Source Firkin
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
Super detailed 16×16 tile that forms a beautiful pattern of straws.
Source Pavel
More bright luxury. This is a bit larger than fancy deboss, and with a bit more noise.
Source Viszt Péter
An attempt for cleaning up the original image in a few steps.
Source Lazur URH
Heavily remixed from a drawing in 'Barbara Leybourne; a story of eighty years ago', Sarah Hamer, 1889.
Source Firkin
From a drawing in 'From Snowdon to the Sea. Striking stories of North and South Wales', Marie Trevelyan, 1895.
Source Firkin