I've learned to never underestimate what PHP and some libraries can do, so for this paper effect, can it be done with a php graphics library (or at least programmatically) without needing something like Photoshop or Illustrator?
To be clear, I'm asking just about the paper, not the iphone.
Edit: Dan Grossman's answer is great. I'm also wondering if someone can give me algorithmic ideas what might be happening in this image so I could try to possibly come up with some code to map it mathematically. My visual imagination is failing me a little.

The answer is always yes, it's just a matter of difficulty/complexity.
PHP is a Turing-complete language, which means it has equal capabilities of every other Turing-complete language, like C++/Java or whatever your photo editing program was written in.
That means whatever Photoshop does, you can do. If nobody has written a handy library, you can treat the image as a matrix and perform the mathematics necessary to get the desired warping, then write the resulting matrix of pixel information to a new image one pixel at a time as a bitmap.
Of course you weren't hoping for that answer, you meant "does someone provide an easy library for PHP to do effects like this with a couple prewritten commands", right?
That's a little much for PHP's GD library, but you can always shell out to a command line image processor, like imagemagick, and read the resulting file to send back to the browser.
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