This was formed by distorting an image of a background on Pixabay.
Source Firkin
From a drawing in 'Gately's World's Progress', Charles Beale, 1886.
Source Firkin
Tiny, tiny 3D cubes. Reminds me of the good old pattern from k10k.
Source Etienne Rallion
Prismatic Hypnotic Pattern No Background
Source GDJ
Prismatic Groovy Concentric Background
Source GDJ
On a large canvas you can see it tiling, but used on smaller areas, it’s beautiful.
Source Paul Phönixweiß
A huge one at 800x600px. Made from a photo I took going home after work.
Source Atle Mo
This one takes you back to math class. Classic mathematic board underlay.
Source Josh Green
Dark blue concrete wall with some small dust spots.
Source Atle Mo
Remixed from a drawing in 'Line and form', Walter Crane, 1914.
Source Firkin
Sometimes simple really is what you need, and this could fit you well.
Source Factorio.us Collective
A pattern drawn in Paint.net and vectorized in Inkscape.
Source Firkin
This ladies and gentlemen, is texturetastic! Love it.
Source Adam Pickering
Small gradient crosses inside 45-degree boxes, or bigger crosses if you will.
Source Wassim
You know I’m a sucker for these. Well-crafted paper pattern.
Source Mihaela Hinayon
The tile this is based on was adapted from an image that was uploaded to Pixabay by frolicsomepl. It can be had in Inkscape by selecting the rectangle and using shift+alt+i
Source Firkin
Prismatic Groovy Concentric Background 2
Source GDJ
Here's a tile-able wood background image for use in web design.
Source V. Hartikainen
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
Zero CC tileable moss or lichen covered stone texture, edited from pixabay. CC0
Source Sojan Janso
Coming in at 666x666px, this is an evil big pattern, but nice and soft at the same time.
Source Atle Mo
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
Smooth Polaroid pattern with a light blue tint.
Source Daniel Beaton