A grid of squares with green colours. Since the colours are randomly distributed it is automatically seamless.
Source Firkin
You guessed it – looks a bit like cloth.
Source Peax Webdesign
Seamless pattern formed from a tile that can be had by selecting the rectangle in Inkscape and using shift-alt-i.
Source Firkin
A free background pattern with abstract green tiles.
Source V. Hartikainen
Here's a seamless brown cork board background texture. Feel free to download or reshare if you like.
Source V. Hartikainen
Geometric triangles seem to be quite hot these days.
Source Pixeden
From a drawing in 'The Quiver of Love', Walter Crane, 1876
Source Firkin
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
Remixed from a design seen in 'Burghley. The Life of William Cecil', William Charlton, 1857.
Source Firkin
From a drawing in 'Art Embroidery', M.S. Lockwood and E. Glaister, 1878.
Source Firkin
A re-make of the Gradient Squares pattern.
Source Dimitar Karaytchev
Carbon fiber is never out of fashion, so here is one more style for you.
Source Alfred Lee
From a drawing in 'Sun Pictures of the Norfolk Broads', Ernest Suffling, 1892.
Source Firkin
Uses spirals from Pixabay. To get the basic tile select the rectangle in Inkscape and use shift+alt+i
Source Firkin
Remixed from a drawing in 'Paul's Sister', Frances Peard, 1889.
Source Firkin
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
Background Wall, Art Abstract, Star Well & CC0 texture.
Source Ractapopulous
I took the liberty of using Dmitry’s pattern and made a version without perforation.
Source Atle Mo