Seamless pattern the tile for which can be had by using shift-alt-I on the selected rectangle in Inkscape.
Source Firkin
Derived from an image that was uploaded to Pixabay by Kaz
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
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
A repeating background of thick textured paper. Actually, it turned out to look like something between a paper and fabric.
Source V. Hartikainen
After 1 comes 2, same but different. You get the idea.
Source Hendrik Lammers
The tile this is based on was adapted from an image that was uploaded to Pixabay by frolicsomepl. It can be had in Inkscape by selecting the rectangle and using shift+alt+i
Source Firkin
From a drawing in 'Art Embroidery', M.S. Lockwood and E. Glaister, 1878.
Source Firkin
Prismatic Snowflakes Pattern 2 No Background
Source GDJ
This tiled background comes in red and consists of tiles that look like gemstones. It is more for blogs or social profiles, I think.
Source V. Hartikainen
This is the remix of "Strawberry Pattern Background" uploaded by "GDJ". Thanks. I realigned strawberries so as to get seamless and changed the BG color.
Source Yamachem
Vector version of a png that was uploaded to Pixabay by pencilparker
Source Firkin
The tile this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i
Source Firkin