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
A seamless pattern the unit cell for which can be had by selecting the rectangle in Inkscape and using shift+alt+i
Source Firkin
Seamless Prismatic Pythagorean Line Art Pattern No Background. A seamless pattern that includes the original tile (go to Objects / Pattern / Pattern To Objects in Inkscape's menu to extract it).
Source GDJ
Did anyone say The Hoff? This pattern is in no way related to Baywatch.
Source Josh Green
To get the tile this is based on select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
Crossing lines with a subtle emboss effect on a dark background.
Source Stefan Aleksić
Prismatic Abstract Geometric Background 5
Source GDJ
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
An abstract texture of water. It's not perfect, but will do. You may download if you like it.
Source V. Hartikainen
Heavily remixed from a drawing in 'Barbara Leybourne; a story of eighty years ago', Sarah Hamer, 1889.
Source Firkin
Here's a subtle marble-like background for use on websites.
Source V. Hartikainen
Geometric triangles seem to be quite hot these days.
Source Pixeden
This was formed by distorting an image of a background on Pixabay.
Source Firkin
From a drawing in 'Art Embroidery', M.S. Lockwood and E. Glaister, 1878.
Source Firkin
This one needs to be used in small areas; you can see it repeat.
Source Luca
Adapted from a drawing in 'Line and form', Walter Crane, 1914.
Source Firkin
From a tile that can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
Derived from elements found in a floral ornament drawing on Pixabay.
Source Firkin
From a drawing in 'Art Embroidery', M.S. Lockwood and E. Glaister, 1878.
Source Firkin
Inspired by this, I came up with this pattern. Madness!
Source Atle Mo
An alternative colour scheme for the original seamless texture formed from an image on Pixabay.
Source Firkin
Derived from an image that was uploaded to Pixabay by Kaz
Source Firkin
Prismatic Geometric Pattern Variation 2 With Background
Source GDJ