This is a high bar to reach.
And a beautiful little app called Tapet performs wonderfully.
It’s an Android app (keep reading if you use iOS!) that actually generates wallpapers on your device. Here’s what the interface looks like:
The checkmark applies the wallpaper, the thumbs up and down help the app decide what qualities to use more often in the randomly generated wallpaper, and you can save it to your phone (but don’t have to, which is nice).
If you’re on Android, you can get Tapet at the Play Store for the low price of nothing.
Further, the app can keep generating new wallpapers for you on a schedule that you determine, so your wallpaper is fresh, but still within the same design aesthetic that you normally like.
Now, I said that iOS people should keep reading, and here’s why: I’ve saved a bunch of wallpapers (and not just ones I’d like) both to give you an idea of what the app can do, but also so that you can snag them and use them on your phone if you choose. You can see them below, or catch the whole set at this Picasa link.