Poladroid

It is a free app for Mac OS X and Windows called Poladroid. I have been using it for years. Or rather I used to use it a lot before I had an iPhone in my pocket at all times. Regardless it's a lot of fun! One of my favorite features is the unpredictable outcome. I have put the same photo in and gotten different results every time.

Here is the same image processed three times.

There are also options to add streaking to the picture and paper in post-processing. I have never played with this much, but in this image you can see it added what looks like a thumbprint.