@robjohn It's a domain-colored plot of a certain theta-like function.

@J.M.isback. It doesn't look a bit simpler to program than some of your other avatars. Not that it isn't colorful and all.

@robjohn Yes, it took a bit of effort to have it come out nicely. Evaluating the function numerically wasn't a cakewalk either.

@J.M.isback. So it's not a builtin function.

At least the structure of its poles and zeroes is clear. :)

@robjohn It's not, indeed.

But the nice thing about it is that ratios of its translates come out to be eliptic functions.

Like that.

@J.M.isback. yeah, I noticed where the contours intersected.

@J.M.isback. searching Google for your avatar gave a lot of colorful results :-)

I'd imagine. :)

The routines in that answer were my starting point; modifying it to have the pictures come out right was the kicker.

Things I didn't know to exist: DifferenceRootReduce, DifferentialRootReduce.

@J.M.isback.: Mathematica 10's color changes have forced some additions that are not backward compatible. I guess I need to check $VersionNumber now...

@robjohn Ha, the plotting changes are the pleasantest of all backward-incompatible changes. Wait till you've encountered the "entitification" and "W|A-fication" of innocent looking (and perfectly working) functions from v9. They managed to squeeze in a Quantity and Entity even where the sun don't shine! :P

@R.M. Why do they do this to us?

Because we are no longer the demographic that they're targeting

Version gated licenses (aka buy once, use forever) are a dying breed and not a predictable source of recurring revenue for the company. Hobbyists are cheap and academics are cheaper and try to stretch the value of their $ by staying on an older version for longer than WRI would like.

There's good money to be made in a subscription based model. The company gets a predictable and recurring source of income, allowing them to iterate faster and push new features/bug fixes to everyone at once, instead of having to wait for a monolithic release with a long and painful QA process and a slower adoption curve. But this also means that they have to fundamentally change who they target (hint: people who like flashy, half-baked stuff that fits in a tweet).

@R.M., I'm only now noticing the Entity[] explosion as a recent adopter. I'm not yet sufficiently annoyed, but maybe it will come in time…

As I once joked, "have they made new Bessel functions in the past year? No? Okay then…" :)

With respect to the new default colors: I haven't yet seen a default that made me want to tear my hair out…

I can't currently name a time when new Entity/Quantity stuff was easier or faster than traditional *Data functions. I can imagine that changing someday though. I made a chart of cumulative population distribution over city size for US and world. Had to strip out Q/E stuff to change comp time from more than 5 minutes to 1 second.

Does someone find the operator for UndirectedEdge (<->) on this page? reference.wolfram.com/language/tutorial/OperatorInputForms.html

@halirutan I don't see it and I guess it would be nice if it was there, especially because we regard that table as the authority on operator precedence (rather than the function Precedence).

@JacobAkkerboom Exactly!

OK, regarding my operator precedence-table the UndirectedEdge is between Equal (290) and Span (305):

@halirutan Precedence[UndirectedEdge] gives 295