ZeroCC tileable mossy (lichen) stone texture, edited from pixabay. CC0
Source Sojan Janso
The green fibers pattern will work very well in grayscale as well.
Source Matteo Di Capua
This is a seamless pattern of regular hexagon which has a honeycomb structure.
Source Yamachem
Real snow that tiles, not easy. This is not perfect, but an attempt.
Source Atle Mo
The name is totally random, but hey, it sounds good.
Source Atle Mo
From a drawing in 'Artists and Arabs', Henry Blackburn, 1868
Source Firkin
A seamless design of flowers remixed from a jpg on Pixabay by Prawny.
Source Firkin
Formed by heavily distorting part of a an image of a fish uploaded to Pixabay by GLady
Source Firkin
Got some felt in my mailbox today, so I scanned it for you to use.
Source Atle Mo
Prismatic Curved Diamond Pattern 7 No Background
Source GDJ
If you want png files of this u can download them here : viscious-speed.deviantart.com/gallery/27635117
Source Viscious-Speed
To get the tile this is based on, select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
One more from Badhon, sharp horizontal lines making an embossed paper feeling.
Source Badhon Ebrahim
Prismatic Abstract Geometric Background 2 No Black
Source GDJ
From a drawing in 'Art Embroidery', M.S. Lockwood and E. Glaister, 1878.
Source Firkin
Medium gray pattern with small strokes to give a weave effect.
Source Catherine
From a design found in 'History of the Virginia Company of London; with letters to and from the first Colony, never before printed', Edward Neill, 1869.
Source Firkin
And some more testing, this time with Seamless Studio. It’s Robots FFS!
Source Seamless Studio
Prismatic Abstract Geometric Background 5
Source GDJ
Textured Red Brown Plastic, Free Background Pattern. Although there's already enough plastic in our lives, let's bring it to the web too.)
Source V. Hartikainen