Heavy depth and shadows here, but might work well on some mobile apps.
Source Damian Rivas
A seamless pattern from a tile drawn in Paint.net and vectorised in Vector Magic
Source Firkin
A seamless background drawn in Paint.net and vectorised with Vector Magic. The starting point was a photograph of drinking straws from Pixabay.
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
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
A seamless background of warped stripes on paper.
Source V. Hartikainen
Prismatic Isometric Cube Extra Pattern No Background
Source GDJ
No relation to the band, but damn it’s subtle!
Source Thomas Myrman
Thin lines, noise and texture creates this crisp dark denim pattern.
Source Marco Slooten
A free seamless background with pink spots.
Source V. Hartikainen
Could remind you a bit of those squares in Super Mario Bros, yeh?
Source Jeff Wall
To get the tile this is based on, select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
Zero CC tileable yellow craft paper; scanned and made by me. CC0
Source Sojan Janso
Green Background Pattern
Source V. Hartikainen
A hint of orange color, and some crossed and embossed lines.
Source Adam Anlauf
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Seamless pattern formed from a tile that can be extracted by selecting the rectangle in Inkscape and using shift-alt-i.
Source Firkin
This background pattern has futuristic look. So, maybe it could be used on websites or blogs dedicated to video games?!
Source V. Hartikainen
Embossed lines and squares with subtle highlights.
Source Alex Parker
From a tile that 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
A seamless tessellation pattern. To get the tile this is formed from, select the pattern in Inkscape and use shift+alt+i.
Source Firkin
Same classic 45-degree pattern, dark version.
Source Luke McDonald
Some dark 45 degree angles creating a nice pattern. Huge.
Source Dark Sharp Edges
Zero CC plastic pattern texture, photographed and made by me. CC0 *Note, this texture was on the perfectly smooth surface of a plastic shovel scraper, not sure how to call it. Plz coment if you know what its called.
Source Sojan Janso