How to get a 13-minute exposure?

what you are attemting to do is exactly what a typical SLR shutter already does. It has two curtains. The first curtain opens the exposure and the second closes it. Most exposures are so short that the closing curtain starts closing the exposure before the opening curtain has fully opened the film. So infact, the exposure is a swipe across the film which is so fast that no movement is apparent. However, if the swipe is slowed down, then a moving subject starts to take on the effect you are talking about. The classic example of this in action is Lartigues racing car wheel.

http://www.masters-of-photography.com/L/lartigue/lartigue_car_trip.html

So, if you could link up the camera shutter curtain to a different timer which also controlled the speed of the curtains, then you would get the effect you are after. You need to be aware which way the curtain is moving, horizontally or vertically.

Easiest way would be to use a large format camera and place your slit moving device inside in the camera just in front of the film plane unless you have the ability to link into the electrics on an SLR and control the shutter that way.

Also read this if you have not already seen it:

http://www.rit.edu/~andpph/text-art+math/index.html

have fun...

[edit]I hate to mention the "D" word here but a scanning back placed on a LF camera would achieve exactly what you want.[/edit]

this sounds similar to the rotating panoramic cameras I play with sometimes...

like someone else said...the shutter speed is actually how long a single spot on the film sees light

with my panoramic cameras the width of my slit affects my exposure...using a narrower slit acts just like a ND filter

I suppose with a really narrow slit you'd get diffraction effects just like with pinhole cameras...so you may want to look into the tables/formulas for optimum pinhole size

anyway, that's my 2 cents

your project reminds me of experiments I did a while back with a FAX machine....the one I took apart turned out to be basically a camera that photographed a narrow strip of the original at a time...I was going to rotate the camera part as the paper fed through to get a panoramic image....but the FAX had a screwed up "paper out" sensor and I never got a decent image -- but I had fun

As has been mentioned, you are going to suffer from massive diffraction problems if the slit is in front of the lens. The slit has to be almost directly next to the film.

I would suggest that with a 13 minute exposure, the slit would be moving so slowly that no part of the film would be exposed without the model moving. That would make the whole image look blurred. Perhaps a one or two second pass of the slit would make the image reasonably sharp and the model could be asked to change expression over that time period.