Carbon Fiber v2 #105
 Carbon  CC BY-SA 3.0

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

 More Textures
Subtle Striped Brown Background Pattern #940
 Stripes  CC BY-SA 3.0

Here's a brown background pattern with subtle stripes. I hope you'll like the color. If not, feel free to change it using an image editor, if you know how of course. Personally, I'm using GIMP to create these backgrounds.

Source V. Hartikainen

regular hexagon pattern #2541
 Grid  CC 0

The image depicts a pattern of regular hexagon.As I made to use it for myself,I want to others to use it.Speaking about the ratio of the image, height : width = 2 : √3(1.732...)Ridiculous to say,I realized later that this image is not honey comb pattern.I have to slide the second row.

Source Yamachem

Decorative divider 217 #2233
 Dark  CC 0

Remixed from a drawing in 'Maidenhood; or, the Verge of the Stream', Laura Jewry, 1876.

Source Firkin

Background pattern 3 #222
 Noise  CC 0

A pattern derived from repeating unit cells each derived from part of a fractal rendering in paint.net.

Source Firkin

Background pattern 235 #2255
 Yellow  CC 0

To get the tile this is formed from select the rectangle in Inkscape and use shift+alt+i.

Source Firkin

Seamless Prismatic Pythagorean Line Art Pattern No Background #569
 Light  CC 0

Seamless Prismatic Pythagorean Line Art Pattern No Background. A seamless pattern that includes the original tile (go to Objects / Pattern / Pattern To Objects in Inkscape's menu to extract it).

Source GDJ

Background Patterns - Ebony #249
 Fabric  CC 0

If you want png files of this u can download them here : viscious-speed.deviantart.com/gallery/27635117

Source Viscious-Speed

Pinstripe #35
 Light  CC BY-SA 3.0

Light gray pattern with a thin pinstripe.

Source Brandon

Background pattern 259 (colour 6) #2097
 Blue  CC 0

Remixed from a design seen on Pixabay. The basic tile can be had by selecting the rectangle in Inkscape and using shift+alt+i

Source Firkin

Snowflake pattern remix #156
 Dark  CC 0

The base gradient edited so now more details are rendered.

Source Lazur URH

Seamless Core Pattern 6 #170
 Dark  CC 0

Seamless Core Pattern 6

Source GDJ