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
Heavily remixed from a drawing in 'Barbara Leybourne; a story of eighty years ago', Sarah Hamer, 1889.
Source Firkin
The base gradient edited so now more details are rendered.
Source Lazur URH
You know you love wood patterns, so here’s one more.
Source Richard Tabor
A seamless pattern from a tile drawn in Paint.net and vectorised in Vector Magic
Source Firkin
If you’re sick of the fancy 3D, grunge and noisy patterns, take a look at this flat 2D brick wall.
Source Listvetra
Prismatic Basic Pattern 2 No Background
Source GDJ
From a drawing in 'Art Embroidery', M.S. Lockwood and E. Glaister, 1878.
Source Firkin
Derived from a PNG that was uploaded to Pixabay by nutkitten
Source Firkin
Prismatic Groovy Concentric Background 3
Source GDJ
The file was named striped lens, but hey – Translucent Fibres works too.
Source Angelica
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
To get the tile this is based on select the rectangle in Inkscape and use shift+alt+i
Source Firkin
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
Prismatic Floral Pattern 3 Variation 3 No Background
Source GDJ
There are many carbon patterns, but this one is tiny.
Source Designova
He influenced us all. “Don’t be sad because it’s over. Smile because it happened.”
Source Atle Mo
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
Same as Silver Scales, but in black. Turn your site into a dragon with this great scale pattern.
Source Alex Parker