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
This is the remix of an OCAL clipart called "Rain on Window" uploaded by "pagarmidna".Thanks.This is a seamless pattern of raindrops.
Source Yamachem
Remixed from a design seen in 'Burghley. The Life of William Cecil', William Charlton, 1857. The tile this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
From a drawing in 'Sun Pictures of the Norfolk Broads', Ernest Suffling, 1892.
Source Firkin
Can’t believe we don’t have this in the collection already! Slick woven pattern with crisp details.
Source Max Rudberg
Seamless pattern the tile for which can be had by using shift-alt-I on the selected rectangle in Inkscape.
Source Firkin
The image depicts a seamless pattern of Japanese Edo pattern called "kikkou-matsu" or "亀甲松" meaning " tortoiseshell-pinetree".The real pinetree is like this: https://jp.pinterest.com/pin/500744052301065077/
Source Yamachem
This one is quite simple in design, it consists of vertical stripes layered on top of a seamless texture.
Source V. Hartikainen
A seamless texture of black leather. I think it will look best when used in headers, footers or sidebars.
Source V. Hartikainen
Remixed from a drawing in 'Maidenhood; or, the Verge of the Stream', Laura Jewry, 1876.
Source Firkin
Just the symbols of the signs of the zodiac distributed in a chequer board-like pattern
Source Firkin
Abstract Tiled Background Extended 8
Source GDJ
Remixed from a drawing in 'Paul's Sister', Frances Peard, 1889.
Source Firkin
Crossing lines with a subtle emboss effect on a dark background.
Source Stefan Aleksić
Hexagonal dark 3D pattern. What more can you ask for?
Source Norbert Levajsics
A simple example on using clones. You can generate a nice base for a pattern fill quickly with it.
Source Lazur URH
This is a seamless pattern of regular hexagon which has a honeycomb structure.
Source Yamachem
Made by distorting a simple pattern using the 'sin waves' plugin for Paint.net and vectorising in Vector Magic
Source Firkin
To get the tile this is based on, select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
Remixed from a design seen in 'Burghley. The Life of William Cecil', William Charlton, 1857.
Source Firkin
Seamless , tileable CC-0 texture. Created by my own, feel free to use wherever you want!
Source Linolafett