[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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