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
Pattern formed from simple shapes. Black version.
Source Firkin
Prismatic Abstract Geometric Background 4
Source GDJ
The original enhanced with one of Inkscapes's filters.
Source Firkin
Recreated from a pattern found in 'Az Osztrák-Magyar Monarchia irásban és képben', 1882. To get the tile this is based on select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
I guess this is inspired by the city of Ravenna in Italy and its stone walls.
Source Sentel
The square tile this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i
Source Firkin
Alternative colour scheme for the original floral pattern.
Source Firkin
No relation to the band, but damn it’s subtle!
Source Thomas Myrman
A pale yellow background pattern with vertical stripes. The stripes are partially faded. I think this background image turned out pretty well, especially those faded stripes.
Source V. Hartikainen
Seamless , tileable CC-0 texture. Created by my own, feel free to use wherever you want!
Source Linolafett
A seamless pattern the starting point for which was a 'light rays' rendering in Paint.net.
Source Firkin
From a drawing in 'Artists and Arabs', Henry Blackburn, 1868
Source Firkin
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
CC0 and a seamless pattern from a tile drawn in Paint.net .
Source SliverKnight
From a drawing in 'At home', J. Sowerby, J. Crane and T. Frederick, 1881.
Source Firkin
A seamless pattern formed from miutopia's cakes on a tablecloth.
Source Firkin
A beautiful dark wood pattern, superbly tiled.
Source Omar Alvarado