The following orange background pattern resembles a honeycomb.
Source V. Hartikainen
A seamless pattern from a tile drawn in Paint.net and vectorised in Vector Magic
Source Firkin
Original minus the background
Source Firkin
Prismatic Polka Dots Mark II 2 No Background
Source GDJ
Prismatic Curved Diamond Pattern 6 No Background
Source GDJ
This seamless background image should look nice on websites. It has a dark blue gray texture with vertical stripes, it tiles seamlessly and, like all of the background images here, it's free. So, if you like it, take it!
Source V. Hartikainen
Derived from an image that was uploaded to Pixabay by Kaz
Source Firkin
Abstract Ellipses Background Grayscale
Source GDJ
Pattern #100! A black classic knit-looking pattern.
Source Factorio.us Collective
Tiny little fibers making a soft and sweet look.
Source Badhon Ebrahim
From a drawing in 'Resa i Afrika, genom Angola, Ovampo och Damaraland', P. Moller, 1899.
Source Firkin
To get the tile this is made up from select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
A monochrome pattern from a tile that can be had by selecting the rectangle in Inkscaope and using shift+alt+i
Source Firkin
A seamless pattern from a tile made from a jpg on Pixabay. To get the tile select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
Remixed from a design on Pixabay. To get the tile this is based on select the rectangle in Inkscape and use shift-alt-i
Source Firkin
Heavy depth and shadows here, but might work well on some mobile apps.
Source Damian Rivas
From a drawing in 'Sun Pictures of the Norfolk Broads', Ernest Suffling, 1892.
Source Firkin
Zero CC tileable ground (#2) cracked, crackled texture, made by me. CC0
Source Sojan Janso
Retro Circles Background 8 No Black
Source GDJ
From a drawing in 'Line and form', Walter Crane, 1914.
Source Firkin
Black & white version of a pattern that came out of playing with the 'light rays' plug-in for Paint.net
Source Firkin
Prismatic Polka Dots 3 No Background
Source GDJ
A frame using leaves from an image that was uploaded to Pixabay by mayapujiati
Source Firkin
The image a seamless pattern derived from a weed which I can't identify.The original weed image is from here:https://jp.pinterest.com/pin/500744052301423641/
Source Yamachem
Dark, crisp and subtle. Tiny black lines on top of some noise.
Source Wilmotte Bastien