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 one needs to be used in small areas; you can see it repeat.
Source Luca
Seamless pattern formed from a tile that can be extracted by selecting the rectangle in Inkscape and using shift-alt-i.
Source Firkin
Small dots with minor circles spread across to form a nice mosaic.
Source John Burks
To get the tile this is based on, select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
Remixed from a drawing in 'Очерки Русской Исторіи въ памятникахъ быта', Petr Polevoi, 1879.
Source Firkin
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
This seamless pattern consists of a blue grid on a yellow background.
Source V. Hartikainen
The tile this is based on can be retrieved by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
Sharp diamond pattern. A small 24x18px tile.
Source Tom Neal
Seamless pattern formed from a tile that can be extracted by selecting the rectangle in Inkscape and using shift-alt-i.
Source Firkin
Dark pattern with some nice diagonal stitched lines crossing over.
Source Ashton
A seamless web background with texture of aged grid paper.
Source V. Hartikainen
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
Prismatic Geometric Tessellation Pattern 3 No Background
Source GDJ
Prismatic Curved Diamond Pattern 2 No Background
Source GDJ
Derived from elements found in a floral ornament drawing on Pixabay.
Source Firkin
Nasty or not, it’s a nice pattern that tiles. Like they all do.
Source Badhon Ebrahim
Here's a quite bright pink background pattern for use on websites. It doesn't look like a real fur, but it definitely resembles one.
Source V. Hartikainen
Floral patterns will never go out of style, so enjoy this one.
Source Lasma
Seamless tile drawn in Paint.net and vectorised in Vector Magic.
Source Firkin