Using prime numbers to make better backgrounds

In the cicada example the point is that one predator would evolve to align its boom cycle so that it had a common divisor with the cycle of the cicada.

Since the predator's cycle is variable, it is evolutionarily optimal if the cicada only comes out every prime number of years.

mryall• 15 years ago

Why can't the predators evolve to have the same cycle as the cicadas, with a prime number of years?

dangoldin• 15 years ago

It's interesting that the cicadas have the cycles they do. Why not also go 23, 29, etc? There's obviously a trade off between being more frequent but also encountering more predators - I'm just curious why they settled on the cycles that they did.

endtime• 15 years ago

Coprimality is still the relevant property. But if one number can be adjusted, then the only way to guarantee coprimality is for the other number to be a prime.

mullr• 15 years ago

They're also useful for reverb effects, in very much the same way. See http://www.npr.org/2010/08/03/128935865/queens-brian-may-roc... (under "On The 'Stomp-Stomp-Clap' Section Of 'We Will Rock You'")

Also, I think the technique will work as long as the numbers are relatively prime, which may be a bit easier to design around.

camtarn• 15 years ago

Using coprime-length looping rhythms on top of each other can also create some pretty interesting sounds.

Take a rhythm in 4/4 (say a standard rock snare backbeat, playing on the second and fourth note of a four note bar), layer on a cymbal pattern which repeats every three notes, then a bass drum pattern which repeats every five notes. The effect is fairly subtle because the snare keeps everything sounding like 4/4, but the feel of the rhythm is constantly shifting.

I found a nice YouTube video demonstrating this a while back, but unfortunately all I can find now is videos of polyrhythms where the loops all have the same duration but different numbers of beats per duration... which is an interesting technique in and of itself :)

adavies42• 15 years ago

Holy shit, Brian May's one more Ph.D. away from being Buckaroo Banzai!

mikesurowiec• 15 years ago

Wow, very impressive! I will definitely be trying this out. It reminded me of my discrete mathematics class, so now I'm wondering if there are any other cool principles that can be applied to design

kylemaxwell• 15 years ago

Fair point, it's really basic combinatorics but well applied and properly executed.

euccastro• 15 years ago

And number theory.

alsomike• 15 years ago

892 unique ways to partition a 3x4 grid: http://www.dubberly.com/concept-maps/3x4grid.html

They also have an interactive tool that generates HTML/CSS: http://www.3x4grid.com

hydrazine• 15 years ago

Gonna try this with pseudo-random opacity styling for even more variations.

mcdaid• 15 years ago

Brilliant interesting article about a very simple but clever idea. I am not sure if I would use this css background technique, but the lego example is brilliant.

Some articles trigger lots of ideas in my mind, this was one of them.

jws3• 15 years ago

I won't get a chance to write this up, but in a similar vein, if you split the grain/texture off of an image, you can scale and stretch the image as needed, then drop a fairly small, tiled grain texture back on top. I think it is nicer to do two grain textures, one for lighter and one for darker. Make the grain image be solid white or black and put the grain in the alpha channel.

xbot3• 15 years ago

Hey guys, I actually mocked up a woodgrain test page while I was developing the article but I ended up preferring the lego and curtain examples. But if your interested:

http://www.sitepoint.com/examples/primes/woodgrain.html

It's not bad, but I don't think it's killer yet.

I've got a very raw maze generation example somewhere if anyone's interested.

prawn• 15 years ago

This is HN. Almost everyone's interested, so post away!

IDisposableHero2• 15 years ago

This is very well explained, but not all that novel. Brian Eno used to generate long soundscapes like this, using loops of mutually prime lengths of time.

Edit: See also -

http://en.wikipedia.org/wiki/Ambient_1:_Music_for_Airports

http://en.wikipedia.org/wiki/Generative_music

nadam2• 15 years ago

Yes it is a known technique also in 3D games. Related, but more complicated (research) topic is infinite/arbitrarily-sized non-looping texture generation from arbitrary sample images.

http://www.cs.sunysb.edu/~vordonezroma/texturesynth.pdf

(There are some mind blowing generated images in the linked PDF.)

jws3• 15 years ago

It also is the core of "method ringing", a kind of bell ringing from the 17th century and persisting today. Imagine some folks clanging away at 10 bells in a church tower for hours on end, never repeating, and never developing a melody. Each person is operating a single bell and repeating their pattern with a unique period.

http://en.wikipedia.org/wiki/Change_ringing

IDisposableHero2• 15 years ago

Hah, that trumps my example by 200 years. Well done.

mturmon• 15 years ago

Ringing the changes uses permutations. The described method uses relatively prime numbers.

Both produce music according to a simple algorithm, but the algorithms are different.

skymt• 15 years ago

The experimental-music band Bull of Heaven recently released a prime-looping generative piece that they project will last 8,462,937,602,125,701,219,674,955.2362595095 years before repeating.

http://bullofheaven.com/media/260.html

SeanLuke• 15 years ago

What's wrong with the "cicada theory"

1. The most common cicadas come out every year or every other year.

2. The 17-year cicadas (for example) don't come out once every 17 years -- they come out every single year. Just in different broods (groups differing by phase). Some broods are much bigger than others of course, and broods are often located in different parts of the country, but many broods can and do overlap.

So I dunno. I'm guessing they're 13 and 17 year cicadas because that's how long it takes to develop.

KirinDave• 15 years ago

Consider, though, that these groups of cicadas don't really "care" about one another from a genetic standpoint. If the broods don't interact, they're basically different sets of genes that only interact via mutations, so the principle still holds.

What's interesting about that is how the broods might diverge to coprime emergence schedules to prevent competition.

ars• 15 years ago

Well, they do care. The idea is to starve out predators. If there is another set of cicadas feeding them, then it doesn't work for just you to avoid them.

scott_s2• 15 years ago

I'm guessing they're 13 and 17 year cicadas because that's how long it takes to develop.

That's a tautology. "A baby takes 9 months to be born because that's how long it takes to develop." Well, yes, but the question becomes, why does it take that amount of time to develop? Were there direct selection pressures acting on that length of time, or is that length of time mostly a function of other variables which are acted on directly by selection pressure?

BrandonM• 15 years ago

This is the perfect Hacker News article. I learned something new and mathematically-interesting about the natural world, the author came up with a clever hack to enliven backgrounds, and we learn how to apply that to improve our own designs.

satori99• 15 years ago

Totally agree. There have been quite a few articles recently that fall into this category.

pquerna's recent post about OpenSSL memory in node (and elsewhere) is another that comes to mind. http://news.ycombinator.com/item?id=2411144

keep 'em coming I say!

TimothyBurgess2• 15 years ago

Upvoted solely for "keep 'em coming!"

This article was truly awesome. I'm kicking myself for having not thought of it before because it seems like such a simple concept! Makes me wonder what else out there I haven't thought of... ;)

derefr• 15 years ago

It's interesting that it's almost impossible to pin down a verbal guideline for what people should be submitting (besides "anything that gratifies one's intellectual curiosity") but pretty easy to point to a given article and say that, yes, this definitely is Hacker News.

It'd be pretty awesome if we could have an HN that's just this sort of stuff (with a strong tendency toward false-negatives vs. false-positives—i.e. no "maybe good", only "definitely good.") I wouldn't mind even if it only had two or three new posts per day—fewer, guaranteed posts means I could actually stand to add it to my RSS reader, vs. the current HN which is more of a firehose: good to stick a bottle in every once in a while, not good to stand in front of.

Thinking on that, here's one way it could be implemented on top of the current HN: if there was some sort of "way, way up"-vote button that (besides being an actual "I wish I had N upvotes to give this" upvote-N-times button) worked as a sort of moral negative to flagging, such that when it had been hit [some threshold] times for an article, the article would get linked into the "/awesome" sublist, that might be enough to make it happen—if we trust the userbase to not abuse it.

If everyone started to way-way-up-vote everything they currently just up-vote, perhaps one could stick a CAPTCHA (or three) on it to make it just annoying enough to disuade abuse (at the cost of further false negatives from people now too lazy to use it.)

gbog• 15 years ago

I dare to disagree. While learning about Cicadas and prime numbers is ok, its application to "enliven backgrounds" seems very futile to me. Hacking means breaking the rules, crack the black box, find new game changing ways to do things that will prove useful for a lot of people. Hacking is not about finding slightly vain design tricks.

In summary, this article is far from what I would upvote. A good indicator of the relative weakness of it is the few interesting comment it triggered.

In fact, some month ago I would come to HN, and read the comments, and find a lot of savoury meat for my curiosity hunger, without even bothering to get check the original article that was only the starting point of high-level exchanges of views on the matter.

PS: Recent articles seem to focus on visual design (pixels and colors), which is very surprising on a website that is so obviously anti-design...

granite_scones• 15 years ago

"This example uses the simplest possible set of prime number — 1, 3, and 7."

1 is not a prime number. Also, the "simplest" possible set of primes would be 2, 3, and 5.

harshpotatoes• 15 years ago

And some people still question the value of pure math. These design tricks would anger some of my design friends, who still believe you can be left brain OR right brain.

TimothyBurgess2• 15 years ago

Yeah what's up with that?! I think in this day and age people are more than capable of being both highly creative and logical.

Nate75Sanders• 15 years ago

While not the same thing, the concept of increasing the degree of realism/getting away from things that are too regular reminded me of Perlin Noise: http://en.wikipedia.org/wiki/Perlin_noise

joubert• 15 years ago

Reminds me of a section in The Blind Watchmaker on cicadas and convergence in evolution - http://books.google.com/books?id=sPpaZnZMDG0C&pg=PA100&#...

jeberle• 15 years ago

Why is it that "design" sites have the worst design? Yes, please be sure to destroy the page margins, and set a min width on the page so that I have to scroll horizontally to read the end of lines. Classic.

Using prime numbers to make better backgrounds

Related Stories