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
Carbon fiber is never out of fashion, so here is one more style for you.
Source Alfred Lee
Remixed from a drawing in 'Chambéry à la fin du XIVe siècle', Timoleon Chapperon, 1863.
Source Firkin
The name tells you it has curves. Oh yes, it does!
Source Peter Chon
Prismatic Curved Diamond Pattern 6 No Background
Source GDJ
Not the most creative name, but it’s a good all-purpose light background.
Source Dmitry
From a drawing in 'Chambéry à la fin du XIVe siècle', Timoleon Chapperon, 1863.
Source Firkin
Another fairly simple design drawn in Paint.net and vectorized in Inkscape.
Source Firkin
A seamless pattern recreated from an image on Pixabay. It is reminiscent of parquet flooring and is formed from a square tile, which can be recovered in Inkscape by selecting the ungrouped rectangle and using shift-alt-I together.
Source Firkin
The green fibers pattern will work very well in grayscale as well.
Source Matteo Di Capua
Prismatic Polka Dots Mark II No Background
Source GDJ
Same as the black version, but now in shades of gray. Very subtle and fine grained.
Source Atle Mo
The square tile this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i
Source Firkin
Continuing the geometric trend, here is one more.
Source Mike Warner
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Looks like an old rug or a computer chip.
Source Patutin Sergey
Here's a repeatable texture that resembles a light green concrete wall or something similar.
Source V. Hartikainen
From a drawing in 'Art Embroidery', M.S. Lockwood and E. Glaister, 1878.
Source Firkin
Prismatic Abstract Geometric Background 2 No Black
Source GDJ
Prismatic Groovy Concentric Background 4
Source GDJ
Seamless pattern the tile for which can be had by using shift-alt-I on the selected rectangle in Inkscape.
Source Firkin