A comeback for you: the popular Escheresque, now in black.
Source Patten
A dark pattern made out of 3×3 circles and a 1px shadow. This works well as a carbon texture or background.
Source Atle Mo
Zero CC bark from fur tree tileable texture, photographed and made by me. CC0
Source Sojan Janso
Some more diagonal lines and noise, because you know you want it.
Source Atle Mo
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
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 was formed by distorting an image of a background on Pixabay.
Source Firkin
Did anyone say The Hoff? This pattern is in no way related to Baywatch.
Source Josh Green
Prismatic Snowflakes Pattern No Background
Source GDJ
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
A free seamless background with pink spots.
Source V. Hartikainen
A simple circle. That’s all it takes. This one is even transparent, for those who like that.
Source Saqib
Colour version of a pattern that came out of playing with the 'light rays' plug-in for Paint.net
Source Firkin
Could be paper, could be a Polaroid frame – up to you!
Source Chaos
Adapted heavily from a JPG that was uploaded to Pixabay by Viscious-Speed.
Source Firkin
Here's an yet another seamless note paper texture for use as a background on websites.
Source V. Hartikainen
Imagine you zoomed in 1000X on some fabric. But then it turned out to be a skeleton!
Source Angelica
From a drawing in 'Cowdray: the history of a great English House', Julia Roundell, 1884.
Source Firkin
Sharp pixel pattern, just like the good old days.
Source Paridhi
Seamless pattern formed from a tile that can be had by selecting the rectangle in Inkscape and using shift-alt-i.
Source Firkin
Remixed from a raster on Pixabay, that was uploaded by ArtsyBee.
Source Firkin