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
The tile for this is based on a repeating unit close to a design on Pixabay. It can be had by selecting the rectangle in Inkscape and using shift-alt-i.
Source Firkin
Prismatic Hexagonalism Pattern No Background
Source GDJ
Prismatic Hypnotic Pattern No Background
Source GDJ
A seamless pattern formed from a square tile. The tile can be retrieved by selecting the rectangle in Inkscape and using shift-alt-I.
Source Firkin
From drawing in 'Musings in Maoriland', Thomas Bracken, 1890.
Source Firkin
From a drawing in 'Gately's World's Progress', Charles Beale, 1886.
Source Firkin
Inspired by a pattern I saw in a 19th century book. This seamless pattern was created from a square tile. To get the tile, select the pattern in Inkscape and use shift+alt+i.
Source Firkin
From a drawing in 'Cassell's Library of English Literature', Henry Morley, 1883.
Source Firkin
Abstract Tiled Background Extended 11
Source GDJ
A new take on the black linen pattern. Softer this time.
Source Atle Mo
Everyone needs some stardust. Sprinkle it on your next project.
Source Atle Mo
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
Seamless , tileable CC-0 texture. Created by my own, feel free to use wherever you want!
Source Linolafett
Submitted as a black pattern, I made it light and a few steps more subtle.
Source Andy
From a design in 'Storia del Palazzo Vecchio in Firenze', Aurelio Gotti, 1889.
Source Firkin
A free pink background pattern.
Source V. Hartikainen
A textured blue background pattern with vertical stripes.
Source V. Hartikainen
Zero CC tileable Crackled Cement (streaks) texture, photographed and made by me. CC0
Source Sojan Janso
Not a pattern for fabrics, but one produced from a jpg of a stack of fabric items that was posted on Pixabay. The tile that this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
Tiny little flowers growing on your screen. Nice, huh?
Source Themes Tube
Alternative colour scheme. Not a pattern for fabrics, but one produced from a jpg of a stack of fabric items that was posted on Pixabay. The tile that this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
Prismatic 3D Isometric Tessellation Pattern 6
Source GDJ