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
Utilising some flowers from Almeidah. To get the unit tile, select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
Formed by distorting an image on Pixabay that was uploaded by gustavorezende. To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
Alternative colour scheme. Not a pattern for fabrics, but one produced from a jpg of a stack of fabric items that was posted on Pixabay. The tile that this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
Number five from the same submitter, makes my job easy.
Source Dima Shiper
Derived from an image that was uploaded to Pixabay by Kaz
Source Firkin
One more in the line of patterns inspired by Japanese/Asian styles. Smooth.
Source Kim Ruddock
Seamless pattern made from a tile that can be obtained in Inkscape by selecting the rectangle and using shift+alt+i.
Source Firkin
Sharp pixel pattern looking like some sort of fabric.
Source Dmitry
Colour version of the original pattern.
Source Firkin
One can never have too few rice paper patterns, so here is one more.
Source Atle Mo
Remixed from an image on Pixabay uploaded by Prawny
Source Firkin
Prismatic Polka Dots Mark II 3 No Background
Source GDJ
A bit of scratched up grayness. Always good.
Source Dmitry
Colorful Floral Background 3 No Black
Source GDJ
Prismatic Floral Pattern 3 Variation 3 No Background
Source GDJ
This was formed by distorting an image of a background on Pixabay.
Source Firkin
Prismatic Snowflakes Pattern 3 No Background
Source GDJ
emixed from a JPG that was uploaded to Pixabay by Kyotime
Source Firkin
Number 5 in a series of 5 beautiful patterns. Can be found in colors on the submitter’s website.
Source Janos Koos