1. we need a realtime renderer. this sequence of “ah, I have a transcendental meromorphic function I want to visualize, I shall type it into my favorite software package and make a picture, and wait to see the result”‘s days is numbered. By the time that rolls around, spending laboriously long time proving extremely persnickety results is going to be dated.
A. it would be good if it could Q or SL(2,Z) highlight images.
B. It would be nice to have a mathematician orientated special functions/fractal platform running over cuda, one that could make things as easy as Adobe Illustrator in some ways.
2. You’ve got a copy of Wegert’s Visual Complex Functions and NIST Handbook of Mathematical Functions, right? Also worth looking at is the Bateman project, Abramowitz and Stegun, Gasper’s book about hypergeometric series, and the Tata lectures on theta functions. It would be nice to start working through that material.
3. You’ve read Jim Belk and Bradley Forrest’s A Thompson Group for the Basilica… it would be nice if we could make videos of these transformations for arbitrary things.
4. Do not trust one renderer. That having been said, we need to agree on a hue model (which is mostly settled at the present?) Why? So we can encode sheaf-theoretic information in it! (Nevanlinna theoretic information as well)
5. If you write a paper about some transcendental meromorphic function which varies on a parameter, make a movie and post it to youtube along with the paper, or on your site.
6. This ‘dip it in formaldehyde, move like insects’ is dangerously slow.
7. Moar pictures. And don’t list points. Make a picture.
8. It would be nice if we could figure out a way for the nonprofessional mathematicians (Burner/Fractaltribe types) to contribute in a meaningful way. But at the moment everything is so Balkanized that there are a lot of disparate communities making very very slow progress on one thing or another.
(I’m sort of at the saddle point between Burners and complex analysts, which makes talking to either somewhat aggravating)