Continuing the geometric trend, here is one more.
Source Mike Warner
Prismatic Hexagonalist Pattern No Background
Source GDJ
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
Prismatic Polka Dots 3 No Background
Source GDJ
A dark background pattern/texture of a dimpled metal plate.
Source V. Hartikainen
One can never have too few rice paper patterns, so here is one more.
Source Atle Mo
Vertical lines with a bumpy, yet crisp, feel to it.
Source Raasa
This is sort of fresh, but still feels a bit old school.
Source Martuchox
A seamless web background with texture of aged grid paper.
Source V. Hartikainen
From a drawing in 'Art Embroidery', M.S. Lockwood and E. Glaister, 1878.
Source Firkin
The rectangular tile this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i
Source Firkin
Same as gray sand but lighter. A sandy pattern with small light dots, and some angled strokes.
Source Atle Mo
A free grid paper background pattern for using on web sites.
Source V. Hartikainen
The green fibers pattern will work very well in grayscale as well.
Source Matteo Di Capua
The tile this fill pattern is based on can be had by using shift+alt+i on the rectangle.
Source Firkin
This background pattern contains a seamless texture of bark. It's not very realistic, but I think it looks quite nice.
Source V. Hartikainen
I love cream! 50x50px and lovely in all the good ways.
Source Thomas Myrman
Awesome name, great pattern. Who does not love space?
Source Nick Batchelor
Crossing lines with a subtle emboss effect on a dark background.
Source Stefan Aleksić
Number 4 in a series of 5 beautiful patterns. Can be found in colors on the submitter’s website.
Source Janos Koos
A set of paper filters. The base texture is generated the same way, only the compositing mode is varied.
Source Lazur URH
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
Seamless pattern the tile for which can be had by using shift-alt-I on the selected rectangle in Inkscape.
Source Firkin
Same as Silver Scales, but in black. Turn your site into a dragon with this great scale pattern.
Source Alex Parker