Here's a quite bright pink background pattern for use on websites. It doesn't look like a real fur, but it definitely resembles one.
Source V. Hartikainen
Sounds French. Some 3D square diagonals, that’s all you need to know.
Source Graphiste
Prismatic Geometric Tessellation Pattern 4 No Background
Source GDJ
A background formed from an image of an old tile on the New York Metropolitan Museum of Art website. To get the base tile, select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
Some dark 45 degree angles creating a nice pattern. Huge.
Source Dark Sharp Edges
An emulated “transparent” background pattern, like that of all kinds of computer graphics software.
Source AdamStanislav
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
You guessed it – looks a bit like cloth.
Source Peax Webdesign
A seamless pattern from a tile made from a jpg on Pixabay. To get the tile select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
Small gradient crosses inside 45-degree boxes, or bigger crosses if you will.
Source Wassim
Classic vertical lines, in all its subtlety.
Source Cody L
Semi-light fabric pattern made out of random pixels in shades of gray.
Source Atle Mo
A seamless pattern based on a tile that can be achieved by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
A pattern formed from a squared tile. The tile can be accessed in Inkscape by selecting the rectangle and using shift-alt-i.
Source Firkin
A grid of squares with green colours. Since the colours are randomly distributed it is automatically seamless.
Source Firkin
Remixed from a drawing that was uploaded to Pixabay by ractapopulous
Source Firkin
Super detailed 16×16 tile that forms a beautiful pattern of straws.
Source Pavel
A seamless green background texture. The image is distributed under a Creative Commons License (like all of the images here).
Source V. Hartikainen
A free seamless background image with a texture of dark red "canvas". It should look very nice on web sites.
Source V. Hartikainen
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
The name Paisley reminds me of an old British servant. That’s just me.
Source Swetha
A blue gray fabric-like texture for websites. An yet another fabric-like texture. It has subtle vertical and diagonal stripes to it.
Source V. Hartikainen
Dark, square, clean and tidy. What more can you ask for?
Source Jaromír Kavan
Nice and simple crossed lines in dark gray tones.
Source Stefan Aleksić