Prismatic Polyskelion Pattern No Background
Source GDJ
Fix and cc0 to get the tile this is based on.
Source SliverKnight
One more in the line of patterns inspired by Japanese/Asian styles. Smooth.
Source Kim Ruddock
A seamless gray background texture suitable for use on websites. To me, it has the look of stone. Feel free to modify it to meet your needs (by making it a bit lighter or darker, for example).
Source V. Hartikainen
Luxury pattern, looking like it came right out of Paris.
Source Daniel Beaton
There are many carbon patterns, but this one is tiny.
Source Designova
An interesting dark spotted pattern at an angle.
Source Hendrik Lammers
From a drawing in 'Cowdray: the history of a great English House', Julia Roundell, 1884.
Source Firkin
To get the tile this is formed from select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
From a drawing in 'Art Embroidery', M.S. Lockwood and E. Glaister, 1878.
Source Firkin
Heavy depth and shadows here, but might work well on some mobile apps.
Source Damian Rivas
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
More in the paper realm, this time with fibers.
Source Jorge Fuentes