From a drawing in 'In an Enchanted Island', William Mallock, 1892.
Source Firkin
Hexagonal dark 3D pattern. What more can you ask for?
Source Norbert Levajsics
Based on several public domain drawings on Wikimedia Commons. This was formed from a rectangular tile. The tile can be accessed in Inkscape by selecting the rectangle and using shift-alt-i.
Source Firkin
More tactile goodness. This time in the form of some rough cloth.
Source Bartosz Kaszubowski
This one has rusty dark brown texture.
Source V. Hartikainen
Remixed from an image that was uploaded to Pixabay by KirstenStar
Source Firkin
A seamless background texture of old cardboard.
Source V. Hartikainen
A simple but elegant classic. Every collection needs one of these.
Source Christopher Burton
Bright Multicolored Floral Background by Karen Arnold from PDP.
Source GDJ
Square design drawn in Paint.net and vectorized in Vector Magic.
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
The square tile this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i
Source Firkin
Here's a camo print with more tan and less green, such as might be used in a desert scenario. This is tileable, so it can be used as a wallpaper or background.
Source Eady
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Dead simple but beautiful horizontal line pattern.
Source Fabian Schultz
To get the tile this is based on select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Prismatic Groovy Concentric Background 3
Source GDJ
Pattern Background, Texture, Photoshop Structure style CC0 texture.
Source Darkmoon1968
A seamless pattern drawn originally in Paint.net by distorting a slice of background pattern 116 and copying the resulting triangle numerous times.
Source Firkin