The prices are listed as crypto currencies, so the payments are on a blockchain. Is the artwork itself sold as a kind of NFT on a blockchain as well? If so, what data is actually stored on the blockchain? The parameters that created the image?

It's also alive and well off the blockchain!

> The kind that would serve coffee in a Klein bottle.

For some definition of "in"

Could title the t-shirt "Topologist's coffee mug!"

The prime field Fₚ can be represented in the complex numbers as the set of roots of the polynomial xᵖ - x.

Now, to build a finite field of size pⁿ, you find an irreducible polynomial P(x) over that prime field and put a field structure on the roots, seen as an n-dimensional vector space over Fₚ.

So all you have to do to map the finite field of size pⁿ to the complex numbers is to find a "good" Fₚ-irreducible P(x) and plot its complex roots. Then you associate points on the curve with such pairs of complex numbers and map them on to the torus as you do with all the rest, marking them as "hey, those are the Fₚ(n)-points of the curve".

In principle, any polynomial P(x) will do; in practice, I suspect some polynomials will serve much better to illustrate the points on the curve than others. We must wait for the follow up paper to see what kind of choices they have made and why.

Their visualizations of elliptic curves over finite fields are the ones that consist of a bunch of discrete points. They then roll those up using some mapping from a complex torus to R^3. There was a time in my life when I might have understood what those words mean, but now I'm just cribbing from the paper.

Do you mean a sphere eversion? :)

Shoutout to my fav math visualization BITD https://www.youtube.com/watch?v=wO61D9x6lNY

You may also enjoy "The geometry of art and life", a 1946 book by Matila Ghyka.

Some texts in the field veer off into sacred geometry territory too swiftly, but I think Ghyka's offers pleasant discussions without.

I would also buy those.

I'd love to see them iterating the values and show the animated versions!