This is a seamless pattern of regular hexagon which has a honeycomb structure.
Source Yamachem
There are many carbon patterns, but this one is tiny.
Source Designova
Prismatic Groovy Concentric Background 4
Source GDJ
Classic vertical lines, in all its subtlety.
Source Cody L
Vector version of a png that was uploaded to Pixabay by pencilparker
Source Firkin
Luxurious looking pattern (for a T-shirt maybe?) with a hint of green.
Source Simon Meek
If you don’t like cream and pixels, you’re in the wrong place.
Source Mizanur Rahman
Heavily remixed from a drawing in 'Barbara Leybourne; a story of eighty years ago', Sarah Hamer, 1889.
Source Firkin
Here's an yet another background for websites, with a seamless texture of wood planks this time.
Source V. Hartikainen
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
From a drawing in 'Codogno e il suo territorio nella cronaca e nella storia'', Gio and Giarella Cairo, 1897.
Source Firkin
A car pattern?! Can it be subtle? I say yes!
Source Radosław Rzepecki
Same as the black version, but now in shades of gray. Very subtle and fine grained.
Source Atle Mo
If you want png files of this u can download them here : viscious-speed.deviantart.com/gallery/27635117
Source Viscious-Speed
A seamless chequerboard pattern formed from a tile that can be had in Inkscape by selecting the rectangle and using shift+alt+i. Alternative colour scheme.
Source Firkin
Not a pattern for fabrics, but one produced from a jpg of a stack of fabric items that was posted on Pixabay. The tile that this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
From a drawing in 'Danmarks Riges Historie af J. Steenstrup, Kr. Erslev, A. Heise, V. Mollerup, J. A. Fridericia, E. Holm, A. D. Jørgensen', 1897.
Source Firkin
From a drawing in 'Chambéry à la fin du XIVe siècle', Timoleon Chapperon, 1863.
Source Firkin
A seamless pattern formed from a sports car on clker.com. To get the tile, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
A background pattern with wavy green vertical stripes. This one has green stripes on a white background. Download if you like it.
Source V. Hartikainen
Never out of fashion and so much hotter than the 45º everyone knows, here is a sweet 60º line pattern.
Source Atle Mo
A seamless pattern formed from a square tile based on a jpg on Pixabay. The tile can be retrieved by selecting the rectangle in Inkscape and using shift-alt-I.
Source Firkin
An aged paper background tile with smeared and pressed text.
Source V. Hartikainen