A seamless pattern the unit cell for which can be had by selecting the rectangle in Inkscape and using shift+alt+i
Source Firkin
Remixed from a drawing in 'Some account of the Worshipful Company of Ironmongers', John Nicholl, 1866.
Source Firkin
It’s like Shine Dotted’s sister, only rotated 45 degrees.
Source mediumidee
From a drawing in 'Resa i Afrika, genom Angola, Ovampo och Damaraland', P. Moller, 1899.
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
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 'At home', J. Sowerby, J. Crane and T. Frederick, 1881.
Source Firkin
Medium gray pattern with small strokes to give a weave effect.
Source Catherine
A seamless pattern formed from a square tile. The tile can be retrieved by selecting the rectangle in Inkscape and using shift-alt-I.
Source Firkin
Prismatic Groovy Concentric Background 5 No Black
Source GDJ
Small dots with minor circles spread across to form a nice mosaic.
Source John Burks
Continuing the geometric trend, here is one more.
Source Mike Warner
From a drawing in 'At home', J. Sowerby, J. Crane and T. Frederick, 1881.
Source Firkin
Almost like little fish shells, or dragon skin.
Source Graphiste
Use shift+alt+i on the selected rectangle in Inkscape to get the tile this is based on
Source Firkin
A background tile for web with abstract repeating texture of dark "stone wall".
Source V. Hartikainen
Geometric triangles seem to be quite hot these days.
Source Pixeden
Colorful Floral Background 3 No Black
Source GDJ
A slightly grainy paper pattern with small horizontal and vertical strokes.
Source Atle Mo
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
Derived from a drawing in 'At home', J. Sowerby, J. Crane and T. Frederick, 1881.
Source Firkin
Seamless , tileable CC-0 texture. Created by my own, feel free to use wherever you want!
Source Linolafett