Not even 1kb, but very stylish. Gray thin lines.
Source Struck Axiom
You know I’m a sucker for these. Well-crafted paper pattern.
Source Mihaela Hinayon
People seem to enjoy dark patterns, so here is one with some circles.
Source Atle Mo
Drawn in Paint.net using the kaleidoscope plug-in and vectorised.
Source Firkin
To get the tile this is made up from select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
The file was named striped lens, but hey – Translucent Fibres works too.
Source Angelica
Alternative colour scheme to the original.
Source Firkin
To get the tile this is based on, select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
From a drawing in 'Jardyne's Wife', Charles Wills, 1891.
Source Firkin
Paper model of a tetrahedron. Modelo de papel de um tetraedro.
Source laobc
A version without colours blended together to give a different look.
Source Firkin
A huge one at 800x600px. Made from a photo I took going home after work.
Source Atle Mo
Not a flat you live inside, like in the UK – but a flat piece of cardboard.
Source Appleshadow
A black tile-able background with paper-like texture.
Source V. Hartikainen
A free seamless background image with a texture of dark red "canvas". It should look very nice on web sites.
Source V. Hartikainen
A pattern formed from a squared tile. The tile can be accessed in Inkscape by selecting the rectangle and using shift-alt-i.
Source Firkin
Remixed from a drawing in 'Line and form', Walter Crane, 1914.
Source Firkin
Prismatic Geometric Pattern Variation 2 With Background
Source GDJ
A dark one with geometric shapes and dotted lines.
Source Mohawk Studios
Original minus the background
Source Firkin
Here's a tile-able wood background image for use in web design.
Source V. Hartikainen
Inspired by an image that was uploaded to Pixabay by geralt
Source Firkin
A free background pattern with abstract green tiles.
Source V. Hartikainen
Remixed from a drawing in 'Chambéry à la fin du XIVe siècle', Timoleon Chapperon, 1863.
Source Firkin