Some more diagonal lines and noise, because you know you want it.
Source Atle Mo
If you want png files of this u can download them here : viscious-speed.deviantart.com/gallery/27635117
Source Viscious-Speed
Farmer could be some sort of fabric pattern, with a hint of green.
Source Fabian Schultz
Number 1 in a series of 5 beautiful patterns. Can be found in colors on the submitter’s website.
Source Janos Koos
A free tileable background colored in off-white (antique white) color.
Source V. Hartikainen
From a drawing in 'Picturesque New Guinea', J Lindt, 1887.
Source Firkin
A seamless texture of an abstract wall colored in shades of light orange brown.
Source V. Hartikainen
The tile this is formed from can be retrieved in Inkscape by selecting the rectangle and using shift+alt+i
Source Firkin
First pattern tailor-made for Retina, with many more to come. All the old ones are upscaled, in case you want to re-download.
Source Atle Mo
Prismatic Polyskelion Pattern No Background
Source GDJ
From a drawing in 'Art Embroidery', M.S. Lockwood and E. Glaister, 1878.
Source Firkin
Just to prove my point, here is a slightly modified dark version.
Source Atle Mo
Drawn in Paint.net and vectorised in Vector Magic.
Source Firkin
To get the tile this is based on, select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
Prismatic Geometric Pattern Background 2 No Black
Source GDJ
Remixed from a drawing in 'Maidenhood; or, the Verge of the Stream', Laura Jewry, 1876.
Source Firkin
ZeroCC tileable moss texture, photographed and made by me. CC0
Source Sojan Janso
Light and tiny, just the way you like it.
Source Rohit Arun Rao
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
Prismatic Floral Background No Black
Source GDJ
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 white version of the very popular linen pattern.
Source Ant Ekşiler
A pattern derived from repeating unit cells each derived from part of a fractal rendering in paint.net.
Source Firkin
From a drawing in 'In an Enchanted Island', William Mallock, 1892.
Source Firkin
With a name this awesome, how can I go wrong?
Source Nikolay Boltachev
Not strictly seamless in that opposite edges are not identical. But they do marry up to make an interesting pattern
Source Firkin