Making Math into Art

January 30, 2023 9:55 AM

A series of posters that visualize all three-digit prime numbers through geometry and color.
posted by duien (18 comments total)

I wish I could buy the Collection 2 posters in quilt form. I love the way the digit colors make a gradient, and how much more clearly visible that is in that particular series. And almost all of them are pretty viable quilt blocks!
posted by duien at 10:01 AM on January 30, 2023

well HELLO
posted by cortex at 10:13 AM on January 30, 2023 [7 favorites]

duien: my partner quilts, and this is one of those things that makes me think I should, until I remember that I have no fine motor skills.
posted by madcaptenor at 10:30 AM on January 30, 2023

Collection 3 would make great ancient/alien languages.
posted by ChurchHatesTucker at 10:38 AM on January 30, 2023 [1 favorite]

I just sent the link to my kids' calc teacher, and suggested she find a large format color printer somewhere in the school.
posted by wenestvedt at 10:49 AM on January 30, 2023

Thanks for the post! These are truly enticing.
posted by crossswords at 10:59 AM on January 30, 2023

This kind of thing is the "first hit is free" of a lot of sometimes-crank amateur number theory. It's beautiful, and there are hints that there must be an awful lot of hidden structure there....
posted by mhoye at 11:33 AM on January 30, 2023 [7 favorites]

Wow, too cool. My fave is Series 1.
posted by Glinn at 12:09 PM on January 30, 2023

These are very beautiful and extremely cool. BUT I really wish the shapes were somehow generated from the 'digital root' they represent. Everything else is so tightly designed that the shapes themselves seem like a loose thread.
posted by TurnKey at 12:15 PM on January 30, 2023 [4 favorites]

This guy has a lot of cool stuff on his website. A web adaptation of the catalog for the ATF Typesetter Model B. A web adaptation of Byrne's Euclid. An explorer for 17th century watercolors.
posted by adamrice at 1:33 PM on January 30, 2023

So before I get negative, let me just say this is cool. Generative art is cool. Graphic design is cool. Geeky math art is cool.

But I wish I liked these better. I finally put my finger on what I don't like: none of the visualizations bring out any structure. They just look like 143 random shapes of a sameness. Which fair enough; prime numbers don't have a lot in common with each other either. But it falls flat for me, I guess I like visualizations that highlight structure more.

The prime visualization I know of that reveals a little structure is Ulam's Prime Spiral and related shapes. That has some structure to it although frustratingly little.
posted by Nelson at 2:25 PM on January 30, 2023 [10 favorites]

Collection 3 Series 1 looks like trawlers from above
posted by swallow at 2:58 PM on January 30, 2023

I don't mean to derail, but if you liked this you might also enjoy these animated factorization diagrams and their source code.
posted by JonJacky at 4:41 PM on January 30, 2023 [2 favorites]

If a visualization doesn’t provide any new information or insights about the underlying data then it’s just a bunch of pretty colors.
posted by schrodycat at 6:39 PM on January 30, 2023 [1 favorite]

JonJacky, I love those visualizations of factors! I just wish I could advance through them step by step instead of constantly pausing and restarting.
posted by The Pluto Gangsta at 8:02 PM on January 30, 2023

Just to be a wet blanket: primes are prime in any number base, but the "digital root"very much depends on the base (in most cases the base is 10). Take 31, which has a digital root of 3+1=4, but in base, uh, say 16 you get 31₁₀=1F₁₆ and the digital root would be (in base 16) 1+F=10, then 1+0 = 1.

So while pretty, I wouldn't take this as a launching point for any new discoveries about primes.
posted by Tad Naff at 9:28 PM on January 30, 2023

The gradients and banding are nice as pure visual features, but... treating prime numbers as collections of decimal digits is a small sin against God. Which is a victimless crime, so.
posted by away for regrooving at 10:36 PM on January 30, 2023 [1 favorite]

Heh, I feel like I'm unusually biased here on a couple differnet fronts but: it's okay to make art based on mathematical notions that isn't, itself, attempting to accomplish the furtherance of mathematical knowledge. Like, every observation above about how this isn't structured in such a way as to reveal new truths about prime numbers is correct! This isn't gonna get basically anything done there. As e.g. Nelson says, it's geeky math art and cool graphic design, and that's about all it is. And all it needs to be!

Because one of the things geeky math art can accomplish, besides extending a core line of mathematical thinking in its own right, is present viewers/readers with an onramp to other smaller elements of math and logic that they might not otherwise have chewed on before. Do digital roots tell us anything about primes as an ordered series? Probably not, certainly not as presented here. But the idea of digital roots itself is interesting; the fact that digital roots of primes are constrained to a subset of possible roots is interesting; the combinatoric vibe of coloring three elements of a common structure according to digit values to encode information more densely is interesting; highlighting combinatoric variation as a mode of visual representation (and the gradients implied by growing digits counts across each poster) is interesting.

It's math art, not a math paper, so focusing on utility is a little off the mark in the first place. But if you want to look at it from that perspective anyway, don't limit the scope of that utility to just serving up an extra helping of details to people already fully engaged on the subject. Art that makes people consider new ideas for the first time, art that gets people to start making their own little leaps and connections, is getting a lot done.
posted by cortex at 7:24 AM on January 31, 2023 [3 favorites]