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
An abstract pale yellow paper-like background with stains colored in yellow and green.
Source V. Hartikainen
Remixed from a drawing in 'The March of Loyalty', Letitia MacClintock, 1884.
Source Firkin
Recreated from a pattern found in 'Az Osztrák-Magyar Monarchia irásban és képben', 1882. To get the tile this is based on select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
From a drawing in 'Art Embroidery', M.S. Lockwood and E. Glaister, 1878.
Source Firkin
Zero CC tileable hard cover cells, skin like, book texture. 4K, Scanned and made by me CC0
Source Sojan Janso
The image depicts a seamless pattern made using a bird's face.
Source Yamachem
A seamless pattern formed from a square tile. The tile can be retrieved by selecting the rectangle in Inkscape and using shift-alt-I. Version with black background.
Source Firkin
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
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
A topographic map like this has actually been requested a few times, so here you go!
Source Sam Feyaerts
Fix and cc0 to get the tile this is based on.
Source SliverKnight
Seamless Prismatic Geometric Pattern With Background
Source GDJ
White circles connecting on a light gray background.
Source Mark Collins
Pixel by pixel, sharp and clean. Very light pattern with clear lines.
Source M.Ashok
Used the 6th circle pattern designed by Viscious-Speed to create a print that can be used for card making or scrapbooking. Save as a PDF file for the best printing option.
Source Lovinglf
The image depicts meshed silhouettes of various things.The original image is an OCAL clipart called "Enter FOSSASIA 2016 #IoT T-shirt Design Contest" uploaded by "openclipart".Thanks.
Source Yamachem
Remixed from an image that was uploaded to Pixabay by KirstenStar
Source Firkin
Seamless pattern the tile for which can be had by using shift-alt-I on the selected rectangle in Inkscape.
Source Firkin
The tile this is based on can be retrieved by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
A seamless gray background texture suitable for use on websites. To me, it has the look of stone. Feel free to modify it to meet your needs (by making it a bit lighter or darker, for example).
Source V. Hartikainen
One of the few full-color patterns here, but this one was just too good to pass up.
Source Alexey Usoltsev
Prismatic Triangular Background Design Mark II 5
Source GDJ
Dark and hard, just the way we like it. Embossed triangles makes a nice pattern.
Source Ivan Ginev