[HN Gopher] Venn Diagram for 7 Sets
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       Venn Diagram for 7 Sets
        
       Author : bramadityaw
       Score  : 158 points
       Date   : 2025-11-04 09:27 UTC (4 days ago)
        
 (HTM) web link (moebio.com)
 (TXT) w3m dump (moebio.com)
        
       | adverbly wrote:
       | Beautiful! I want to get this on a t-shirt!
        
       | anon291 wrote:
       | Nice! 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 wrote:
         | It is possible for arbitrary N; one construction is called the
         | Edwards-Venn diagram. See
         | https://happyruin.wordpress.com/2013/03/24/edwards-venn-diag...
        
       | vitalnodo wrote:
       | I'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/
        
         | zem wrote:
         | the comments here 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 wrote:
         | The nVennR library is pretty robust for multiple sets
         | 
         | https://venn.bio-spring.top/intro#nvennr
        
         | qustrolabe wrote:
         | https://www.deepvenn.com/
        
       | cubefox wrote:
       | The website isn't working for me (Android Firefox/Chrome).
        
         | akdor1154 wrote:
         | Nor Firefox Android, even in Desktop mode.
        
         | JoBrad wrote:
         | Same for iOS.
        
       | keeeba wrote:
       | Please don't actually use these 5,6,7-way Venn diagrams for
       | anything practical, they're virtually useless and communicate
       | nothing.
        
         | paulddraper wrote:
         | Thanks, I was just about to do that!
        
         | roadside_picnic wrote:
         | Technically 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
        
         | emmelaich wrote:
         | Agree, I think the linked Upset diagram is better.
        
         | somat wrote:
         | There 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
         | 
         | However you could make a good argument that having a
         | complicated and confusing diagram is the point of that puzzle.
        
       | kugestu wrote:
       | Really nice theoretical exercise! For practical visualization, an
       | UpSet plot is a great option: https://upset.app/
        
         | renewiltord wrote:
         | Required attribution notice too big. Can't see myself using it.
        
         | JSR_FDED wrote:
         | TIL! Upset plots are useful and easy to understand.
        
       | flobosg wrote:
       | Related: the 6-set banana Venn diagram -
       | https://www.nature.com/articles/nature11241/figures/4
        
         | Amorymeltzer wrote:
         | Still my favorite Venn.
         | 
         | I was in a genetics graduate program when this was published,
         | and this spread like wildfire.
        
       | irchans wrote:
       | I think this 6 set Venn Diagram is nice because I made it. :)
       | 
       | http://162.243.213.31/wp-content/uploads/2012/08/Ven3.png
        
         | stogot wrote:
         | How 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 wrote:
           | Looks like sinusoids in polar coordinates
        
           | irchans wrote:
           | Type "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-b598-41fe487b4e.
           | ..
           | 
           | 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 wrote:
       | Can this be configurable? Like 8..9..etc
        
       | thadk wrote:
       | Here's a very rough interactive on more recently published 7-way
       | and 11-way 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
       | 
       | Santiago Ortiz's venn was from 2013 (via archive.org) . I had
       | forgotten I'd seen that, thanks for sharing.
        
       | pierrec wrote:
       | The 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
        
       | fainpul wrote:
       | Of 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 wrote:
         | Ovals, arguably roundish, can do 4 sets well in 2D.
        
           | fainpul wrote:
           | Right. 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_hig.
           | ..
        
       | jesperwe wrote:
       | I 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 wrote:
         | I 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 wrote:
       | Rendering and functionality is broken on iOS Safari
        
       | haritha-j wrote:
       | For 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-d...
        
         | Jaxan wrote:
         | In 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.
        
           | amelius wrote:
           | The three lightgray circles in the examples are the empty
           | set.
        
           | bmm6o wrote:
           | One example included the empty set, the other did not. It
           | doesn't always make sense to have it.
        
         | leontrolski wrote:
         | Ditto, another Upset blog post -
         | https://leontrolski.github.io/upset.html
        
         | turnsout wrote:
         | TIL 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 wrote:
       | Beautiful (on desktop)!
       | 
       | On mobile it is uncanny valley - I see something, but it is
       | broken.
        
       | lisper wrote:
       | > 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 wrote:
         | Those colors are similar but obviously distinct to me. Maybe
         | your monitor is the issue?
        
           | lisper wrote:
           | I thought of that. I'm on a Macbook Air and initially I had
           | Night Shift on but even after I disabled it I still couldn't
           | tell the difference.
        
         | jessriedel wrote:
         | I 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 wrote:
       | Yeah, 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.
        
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       (page generated 2025-11-08 23:01 UTC)