The Picturebook is about illustrating mathematical picture stories. The Puppetshow is about animating them. The modifiers refer to the fact that hand-drawn pictures are topological objects, while computer animations require precise geometrical description.
In the meantime, here is a web version of a powerpoint presentation given at Bologna last fall. It has lots of pictures, some animations, and one movie which takes 3 minutes to load even on a cable modem, and which you might want to skip. Also, for now it can be viewed only on a late model Microsoft browser because it was made with a Microsoft slide-to-web utility. So you should look generic jpeg version of the same slides. This is the version I'll be adding comments to, anyway.
A theoretical formulation, Metarealistic Rendering of Real-time Interactive Computer Animations, was presented at the Mosaic 2000: Millennial Open Symposium on the Arts and Interdisciplinary Computing in Seattle last August and an expanded version will appear in Michele Emmer's Visual Mind 2 next year.
The Buckingham Lectures at Miami University in Athens, Ohio, provided a wonderful audience for a leisurely look at both illustration and animation.