A huge one at 800x600px. Made from a photo I took going home after work.
Source Atle Mo
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
You don’t see many mid-tone patterns here, but this one is nice.
Source Joel Klein
A grid of squares with green colours. Since the colours are randomly distributed it is automatically seamless.
Source Firkin
Formed from a tile based on a drawing from 'Viaggi d'un artista nell'America Meridionale', Guido Boggiani, 1895.
Source Firkin
Colour version that is close to the original drawing uploaded to Pixabay by pencilparker.
Source Firkin
From a drawing in 'Sun Pictures of the Norfolk Broads', Ernest Suffling, 1892.
Source Firkin
Simple combination of stripy squares with their negatively coloured counterparts
Source Firkin
There are many carbon patterns, but this one is tiny.
Source Designova
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
From a drawing in 'Art Embroidery', M.S. Lockwood and E. Glaister, 1878.
Source Firkin
Tiny, tiny 3D cubes. Reminds me of the good old pattern from k10k.
Source Etienne Rallion
Zero CC tileable seed texture, edited by me to be seamless from a Pixabay image. CC0
Source Sojan Janso