How does an iOS screensaver app work?
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A client of mine recently came up with a few apps he came across while browsing online.  Specifically, he discovered that there are apps that call themselves 'screensavers', and now he wants me to make him a screensaver app.

The obvious problem is that I don't know of any way to make my app open (displacing whatever is in the background) based on a lack of user input in another app!  In fact, I would have sworn that it was completely impossible to do so.

So, to wrap up the question -- is it possible to make such an app, and if so how?  Or are those apps really, really, badly labeled?