The science of pinholes is covered in my previous Instructable
if you are new to pinhole cameras I recommend you read this Instructable before continuing if you want to fully grasp the concepts shown here.
Now that you've seen the results, you're probably pretty confused. I'll do my best to explain whats going on here but it is very unconventional. The film is held in a cylinder instead of a flat plane like in a conventional camera. As a result, the pinhole is projecting an image onto a non-flat object. This inherently causes image distortion, like the way road lines look short when driving and long when on the sidewalk. Then once the film is unrolled the image appears even more distorted.
The resulting image has lost the center of the scene, and the rest of the scene has been contorted from a round image into a rectangular one as illustrated by the red and blue lines in the image below.
Because these resultant images are so distorted it is very difficult to imagine how the scene will end up when preparing to take a photograph. It is almost entirely up to luck but a key point is to have the scene full of objects, because bland things like the blue sky will not show the distortion the way buildings or trees do.
When it comes to designing an anamorphic pinhole camera, there are some modifications to the standard rules of pinhole design. Basically, the focal length of the pinhole should be at the far end of the film, and the near end of the film should be inside the maximum image cone that the pinhole produces. The pinhole I used is 0.3mm diameter, and in 0.003" material, resulting in a 150 degree image cone. The resulting design captures things in the image from 41 to 129 degrees from center.
Since the film is closer to the pinhole at one end and farther at the other, the effective aperture of the pinhole changes with this distance, but since the closer film is at a wider angle to the pinhole, the pinhole's effective diameter is reduced, so it does not become over exposed. Its an imprecise science but it works pretty well.