Thursday, April 30, 2009

Slouching towards Adelaide

At some point when I was in grad school I became aware of some work on symmetric Venn diagrams. If you google this, you will find this link, which has been maintained but not changed too much since 1997. Other than that, there isn't a lot on the web and there is a particular lack of quantitative direction on how to construct the beautiful rotationally symmetric Venn diagrams such as Adelaide. This was named by Anthony Edwards after the city in which he discovered it. I have always wanted to go to Adelaide, it holds a strange attraction for me, so perhaps that is why that particular 7-set Venn diagram stuck in my head.

When I started working on my coloring book, I immediately thought of the Adelaide diagram but I didn't know how to construct it. After some mistakes today, I think I finally have it down. Here is a colored version:

Code (in Sage) for some version of this will be in the final coloring book.


kab said...

I have never heard bevor of Venn diagrams, but I must admit that they are beautiful. Nicely done!

Alec Jacobson said...

Does your formula expand (and contract) well to any N-size venn diagram?

(This one is beautiful, I needed to look close to really appreciate it)

M. Hampton said...

Anthony Edwards did create a sort of construction for arbitrary N, but not for the rotationally symmetric diagrams like Adelaide.

There is a pretty crazy-looking construction for N=11: