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
Prismatic Groovy Concentric Background 2
Source GDJ
Zero CC tileable seed texture, edited by me to be seamless from a Pixabay image. CC0
Source Sojan Janso
Awesome name, great pattern. Who does not love space?
Source Nick Batchelor
Abstract Stars Geometric Pattern Prismatic No Background
Source GDJ
The file was named striped lens, but hey – Translucent Fibres works too.
Source Angelica
Scanned some rice paper and tiled it up for you. Enjoy.
Source Atle Mo
A light gray fabric pattern with faded vertical stripes.
Source V. Hartikainen
From a drawing in 'Worsborough; its historical associations and rural attractions', Joseph Wilkinson, 1879.
Source Firkin
Love the style on this one, very fresh. Diagonal diamond pattern. Get it?
Source INS
Snap! It’s a pattern, and it’s not grayscale! Of course you can always change the color in Photoshop.
Source Atle Mo
This one is so simple, yet so good. And you know it. Has to be in the collection.
Source Gluszczenko
Formed from a tile based on a drawing from 'Viaggi d'un artista nell'America Meridionale', Guido Boggiani, 1895.
Source Firkin
This was formed by distorting an image of a background on Pixabay.
Source Firkin
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
A free seamless background image with abstract texture of green "curtain".
Source V. Hartikainen
Heavy depth and shadows here, but might work well on some mobile apps.
Source Damian Rivas
Actually remixed from a pattern on Pixabay. But then noticed a very similar one on Openclipart.org uploaded by btj51q2.
Source Firkin
A large pattern with funky shapes and form. An original. Sort of origami-ish.
Source Luuk van Baars
Super simple but very nice indeed. Gray with vertical stripes.
Source Merrin Macleod
Light gray grunge wall with a nice texture overlay.
Source Adam Anlauf
Fix side and a seamless pattern formed from circles.
Source SliverKnight