PolyGen is a free (with one in-app purchase) universal app that creates attractive wallpapers with a single tap. If you don't like the design, tap again. When you are finally happy with the generated design, you can export it to your camera roll, mail it, or send it via the Messages app.
PolyGen generates polygon-based designs based on a built-in formula. The chosen colors seem to relate well, so the wallpaper is never garish. Some people might want to use a photo editor to blur the background.
Each generated pattern is unique. With a US$0.99 in-app purchase, you can seed the generator with colors you select and choose cell size and the type of gradients. I was satisfied with the free version, but I can see where some people might want to exercise more control, and the extra features are inexpensive.
There are a lot of other wallpaper apps around, of course. Most provide a static library of photos and designs; some, like the free Wallpaper Designer HD, give you basic surfaces you can modify.
PolyGen is a useful app which gives your iOS home and lock screens a look you can constantly freshen up. The free app does display ads at the top of the screen, but I did not find them to be intrusive. The app requires iOS 6.0 or later, and is optimized for the iPhone 5.
PolyGen: Create unique new iOS wallpapers with a tap
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