The 5-set Venn diagram looks beautiful (and is apparently by Branko Grünbaum), but is a similar symmetric 4-set Venn diagram also possible? Can't find any such example on the internet
EDIT: apparently not, from Wikipedia: "David Wilson Henderson showed, in 1963, that the existence of an n-Venn diagram with n-fold rotational symmetry implied that n was a prime number."
I've had an inkling at various times to make a widget or app or something for players of Diplomacy [0] that uses this visualization to make it easier to see activity in all of your conversations at a glance / select who to talk to. It always ends up being more of a 'fun' idea than something that would actually be useful, though, because the 6-set Venn diagram is so much more difficult to visually parse than just a list of countries in a "To" line.
[0] when played with "white press", which is where players can send messages to another player / to multiple other players, and the source of the message is authenticated. This is in contrast to "gray press" where the source is / can be anonymous instead of authenticated and "black press" where the source can be spoofed.
This would almost certainly be more difficult, but I'd love if the diagram's relative sizes (optionally) accounted for the size of the sets' data – e.g. if set A and B have 2 items each with zero overlap, it would show two circles of equal size, completely apart from one another
I've used this before, it's a cool idea but it only sort of works. For most non-trivial examples, there will be still be a big discrepancy between the visual area of overlaps and the and the actual element count. Claiming that the graph is area-proportional might actually be more misleading if it's not actually accurate.
To improve it, you'd need more ways to mutate the shapes to try to find a solution with less error. E.g. if the circles could be squashed into ellipses, that would probably help. Of course, some higher-order graphs can't be shown with convex shapes at all, so you'd ideally want to be able to pull and stretch areas as needed. It's a hard problem.
Wow, that 6-set visualization feels more asymmetric than 2,3,4,5. Is there an upper bound to the number of sets you can visualize in 2D, and how about 3D?
I was at ISMB [0] and BOSC [1] conferences earlier this month and Venn and Euler diagrams were all over the poster session. Not sure why, but biologists love them!
I wrote an implementation of Venn and Euler diagrams for the bioinformatics data visualization application Cytoscape many years ago [2]. Sigh, thick clients in Java haven't aged all that well.
[0]: https://www.youtube.com/watch?v=edDnGiJStvs