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Venn Diagram for 7 Sets
- adverbly 11mo agoBeautiful! I want to get this on a t-shirt!
- anon291 11mo agoNice! I wonder if there's a mathematical theorem to describe the possible shapes for a 2-d venn diagram of N sets or if there's an N for which it is no longer possible (or maybe it's possible for all N!?). Probably an application of graph theory and Euler's formula to determine feasibility and then something else to figure out the shape constraints. Never thought about it, but an interesting idea.
- madcaptenor 11mo agoIt is possible for arbitrary N; one construction is called the Edwards-Venn diagram. See https://happyruin.wordpress.com/2013/03/24/edwards-venn-diagrams/ https://happyruin.wordpress.com/2013/03/24/edwards-venn-diag...
- vitalnodo 11mo agoI’m wondering what’s the proper way to draw Venn diagrams. I’ve seen that Graphviz has a “nice to have” mention about them, and there are a few simple JS libraries - mostly for two sets. Here’s also my own attempt using an LLM [1]. But maybe someone knows a more general or robust solution - or a better way to achieve this? In the future, I’d like to be able, for example, to find the intersection between two Venn diagrams of three sets each etc. [1] https://vitalnodo.github.io/FSLE/ https://vitalnodo.github.io/FSLE/
- zem 11mo agothe comments here https://news.ycombinator.com/item?id=45742907 https://news.ycombinator.com/item?id=45742907 have some discussion about projects that take a "focused algorithm for various different diagram types" approach vs graphviz's one size fits all approach. worth checking to see if any of them do venn diagrams.
- tetris11 11mo agoThe nVennR library is pretty robust for multiple sets https://venn.bio-spring.top/intro#nvennr https://venn.bio-spring.top/intro#nvennr
- qustrolabe 11mo agohttps://www.deepvenn.com/ https://www.deepvenn.com/
- cubefox 11mo agoThe website isn't working for me (Android Firefox/Chrome).
- TheRealNGenius 11mo ago[dead]
- keeeba 11mo agoPlease don’t actually use these 5,6,7-way Venn diagrams for anything practical, they’re virtually useless and communicate nothing.
- paulddraper 11mo agoThanks, I was just about to do that!
- roadside_picnic 11mo agoTechnically a Venn diagram's entire point is to visualize all possible set relations between N sets. Their "practical" use is explicitly visualizing this. In popular terminology they are very often confused with Euler Diagrams [0] which represent meaningful relations in sets but not all possible. You shouldn't create Euler Diagrams this complex, but the raison d'etre of Venn diagrams is to visualize the complex nature of set relations. 0. https://en.wikipedia.org/wiki/Euler_diagram https://en.wikipedia.org/wiki/Euler_diagram
- emmelaich 11mo agoAgree, I think the linked Upset diagram is better.
- somat 11mo agoThere is always the complicated wires puzzle from "Keep Talking and Nobody Explodes". Where a 5 way Venn diagram encodes what action you need to take for a given state. https://bombmanual.com/web/index.html#ComplicatedWires https://bombmanual.com/web/index.html#ComplicatedWires However you could make a good argument that having a complicated and confusing diagram is the point of that puzzle.
- kugestu 11mo agoReally nice theoretical exercise! For practical visualization, an UpSet plot is a great option: https://upset.app/ https://upset.app/
- renewiltord 11mo agoRequired attribution notice too big. Can’t see myself using it.
- JSR_FDED 11mo agoTIL! Upset plots are useful and easy to understand.
- flobosg 11mo agoRelated: the 6-set banana Venn diagram – https://www.nature.com/articles/nature11241/figures/4 https://www.nature.com/articles/nature11241/figures/4
- Amorymeltzer 11mo agoStill my favorite Venn. I was in a genetics graduate program when this was published, and this spread like wildfire.
- irchans 11mo agoI think this 6 set Venn Diagram is nice because I made it. :) http://162.243.213.31/wp-content/uploads/2012/08/Ven3.png http://162.243.213.31/wp-content/uploads/2012/08/Ven3.png
- stogot 11mo agoHow did you make this? It is nice. Why does the red line have a heart-shaped bounce/curve in the open white space instead of just being round?
- recursive 11mo agoLooks like sinusoids in polar coordinates
- irchans 11mo agoType "Polar plot 6 curves of the form r = (1 + Sin[2^(k - 1) t]/2^(k - 1)) where k =1, 2, .., 6 and t=0 to 2 Pi each curve should be a different color" into ChatGPT5. https://chatgpt.com/share/690f675d-c340-8013-b598-41fe487b4ea1 https://chatgpt.com/share/690f675d-c340-8013-b598-41fe487b4e... It has the nice properties that you can do any number of sets (in theory) and all the boundary intersections are either osculating or perpendicular.
- Sparkenstein 11mo agoCan this be configurable? Like 8..9..etc
- thadk 11mo agoHere's a very rough interactive on more recently published 7-way and 11-way venn: https://observablehq.com/@thadk/venn https://observablehq.com/@thadk/venn (with clean-ish svg, cites) This fork shows an older version with all the shapes turned on and filled with original colors: https://observablehq.com/d/4a5120e490fa9da4 https://observablehq.com/d/4a5120e490fa9da4 Santiago Ortiz's venn was from 2013 (via archive.org) . I had forgotten I'd seen that, thanks for sharing.
- pierrec 11mo agoThe source has a distinct face-melting vibe. Judging from leftover variables, seems like part of the original plan was to make a 7-way Venn diagram of these broad disciplines: "ART INTERFACE SCIENCE LANGUAGE TECHNOLOGY HUMANISM NETWORKS". The possible resulting combinations also seem to have remained in the code, going from tame concepts like "illustration" and "games", down to gems like "folksonomy", "hypernarrative", "facebook" (??) https://moebio.com/research/sevensets/Main.js https://moebio.com/research/sevensets/Main.js
- fainpul 11mo agoOf course nice / "proper" / usable Venn diagrams use only round(-ish) shapes so they are easy to decipher. If you stick to this limitation, you can visualize up to 3 sets in 2D (using circles), 4 sets in 3D (using spheres), then it gets tricky...
- pohl 11mo agoOvals, arguably roundish, can do 4 sets well in 2D.
- fainpul 11mo agoRight. I don't find that clear anymore. Seems more like a puzzle to me. The 3D one works somewhat well if the spheres are translucent and animated. https://en.wikipedia.org/wiki/Venn_diagram#Extensions_to_higher_numbers_of_sets https://en.wikipedia.org/wiki/Venn_diagram#Extensions_to_hig...
- jesperwe 11mo agoI wonder why when swipeing between the two sides of the disc it always appears convex from the currently viewed side, but flat when viewed edge on. Anyone knows what could cause this?
- hashmal 11mo agoI think it's to avoid having two sets of data points. I think the "view angle" affects the "convex amount" so that edge-view = flat and all other viewing angles "bump" the data points a little bit to give the "convex" look.
- moi2388 11mo agoRendering and functionality is broken on iOS Safari
- haritha-j 11mo agoFor usable diagrams, beyond 3 sets, I always recommend upset plots, I wrote a little piece on them rather recently: https://medium.com/@harithajayasinghe/beyond-venn-diagrams-diving-into-upset-plots-2283db377fb0 https://medium.com/@harithajayasinghe/beyond-venn-diagrams-d...
- Jaxan 11mo agoIn all these pictures, the empty set is missing (-: . Of course you could argue that they’re also missing in Venn diagrams, but it’s common to just point on the outside.
- leontrolski 11mo agoDitto, another Upset blog post - https://leontrolski.github.io/upset.html https://leontrolski.github.io/upset.html
- turnsout 11mo agoTIL about upset plots. Really cool! Venn is already unwieldy at three sets, but four is not really doing the job of communicating the set inclusion clearly. Seven is just a geometric curiosity.
- stared 11mo agoBeautiful (on desktop)! On mobile it is uncanny valley - I see something, but it is broken.
- lisper 11mo ago> I decided to use colors rather than numbers or letters to identify each basic set, though I didn't use the same colors Newton did; mine are equidistant in the hue circle. "Lawn green" and "medium spring green" look completely identical to me. Maybe I have a really obscure kind of color blindness?
- bobsmooth 11mo agoThose colors are similar but obviously distinct to me. Maybe your monitor is the issue?
- jessriedel 11mo agoI have normal vision. I wouldn't say completely identical when they are side-by-side, but they are very close. It's effectively impossible to discriminate them when they are not side-by-side, which for this plot is very important. The author's mistake was this: "[my colors] are equidistant in the hue circle". The problem is that the hue circle (at least under the parameterization scheme he used) is not uniform over discrimination, i.e., the ability to discriminate two hues is not invariant under displacing them an equal amount along the circle. (I presume this is one of those situation where it's misleading to think about three primary colors on equal footing because of quirks of human vision biology.) First, the author could have chosen 7 hues at max-saturation that were easier to discriminate than this. But more importantly, he should have used the other color axes: saturation and brightness. dark red (~maroon) and light red (~pink) are a lot easier to discriminate, even when not next to each other, than the two shades of green he used.
- pohl 11mo agoYeah, I know that Upset Plots are a better choice for data visualization — as everyone is pointing out — but take a moment to appreciate this beautiful etude for what it is. This nicely executed. I love how this forced the author into some very difficult choices about how to create a large set of convincingly "mixed" colors — which is a very difficult problem even with just 4 overlapping base colors! In some sense, they "lucked out" by dealing with a prime number of primary color sets, which helped them avoid having multiple pairs of colors that are directly across the wheel from each other. Very nicely done. It's fun to play with, and inspiring to study.