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.
PolyGen for iOS
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.