Who says apps are only for older babies and kids? I've been using High Contrast Patterns and Shapes for newborns on my daughter since she was born two weeks ago and she really seems to engage with it!
This app is designed to stimulate a newborn since they can't focus their eyes completely yet. It has black-and-white patterns set to a classical music track that is soothing and gentle. My little lady likes to stare at it - although she only does so for about 5 minutes max. Still, it's fun to watch her watch these patterns so intently. And it affords me time to brush my teeth, which is worth the $1.99 app price in and of itself!
This app works for iPad, iPhone, and iPod Touch. Download it here!