pi in pixels

October 26, 2006 10:31 AM

what happens if you assign a colored pixel to each decimal of pi?
posted by petsounds (99 comments total)

If you squint, it says, "Drink Coke."
posted by weapons-grade pandemonium at 10:34 AM on October 26, 2006

Paul's dead?!
posted by matthewr at 10:35 AM on October 26, 2006

Good illustration of "chaos" vs. "noise". Nothing random about it, and yet it looks like static.
posted by LordSludge at 10:36 AM on October 26, 2006 [1 favorite]

[n3rDfilter]

btw, a two dimensional image is clearly not how one would want to visualize this, even if they were expecting a clever pattern.

conclusion: this nerd wasnt thinking very hard.
posted by mano at 10:36 AM on October 26, 2006

You would need an infinitely large screen resolution to show a colored pixel for each digit of pi. And it would still be kind of a crappy post.
posted by Mister_A at 10:37 AM on October 26, 2006

Those ad agencies are getting more shameless by the minute. Damn those sell-out mathematicians.
posted by Zero Gravitas at 10:38 AM on October 26, 2006

pi overdone
posted by It's Raining Florence Henderson at 10:41 AM on October 26, 2006

Wow, it looks exactly like what you'd expect the decimal expansion of a roughly normally distributed transcendental number to look like.
posted by sonofsamiam at 10:41 AM on October 26, 2006 [1 favorite]

He got the 107,254^th digit wrong; it was suppsed to be 7.
posted by ZenMasterThis at 10:41 AM on October 26, 2006 [1 favorite]

It's a sailboat!
posted by Faint of Butt at 10:42 AM on October 26, 2006

It's supposed to be nine, not seven.
posted by Keith Talent at 10:43 AM on October 26, 2006

Actually, I thinks it's one of those 3D magic eye pictures, stare at it long enough and unfocus your vision.
posted by Keith Talent at 10:44 AM on October 26, 2006

Snow Crash
posted by It's Raining Florence Henderson at 10:45 AM on October 26, 2006 [1 favorite]

I can see my house!
posted by loquacious at 10:46 AM on October 26, 2006

I think that's my house. Or a llama, but why would a llama be wearing a bullfighter's 'suit of lights' and carrying an enormous mercury arc rectifier?
posted by loquacious at 10:48 AM on October 26, 2006

Way to trip up mathematicians with synesthesia, dude.
posted by maudlin at 10:48 AM on October 26, 2006 [1 favorite]

I saw this on TV last night.
posted by hal9k at 10:49 AM on October 26, 2006 [2 favorites]

There used to be a site called www.amigodornot.net (no link as it's gone now) where people would vote on a randomly-generated picture of noise, just like this, as to whether it was an accurate picture of God.

The reasoning being, of course, that at some point in infinity a truly random number generator would create up a picture of God.

So I guess this is a good a picture of God as any.

Has anybody tried to make a picture of 'e'? Perhaps if you overlay the two you get "ZAPHOD BEEBLEBROX WAS HERE".
posted by randomination at 10:50 AM on October 26, 2006 [1 favorite]

The Big Bang's Playing on TV

Several members of the NASA Goddard COBE team work on WMAP. Like COBE, WMAP scans the sky over and over again, soaking up the ancient light from the Big Bang known as the cosmic microwave background. Microwaves are a low-energy form of radiation but higher in energy than radio waves. The cosmic microwave background blankets the universe and is responsible for a sizeable amount of static on your television set--well, before the days of cable. Turn your television to an "in between" channel, and part of the static you'll see is the afterglow of the big bang.

from nasa.gov
posted by Kelly Tulsa at 10:51 AM on October 26, 2006 [1 favorite]

Staring at that is making me pi-eyed.
posted by googly at 10:52 AM on October 26, 2006

I want to see what i looks like.
posted by Mister_A at 10:53 AM on October 26, 2006

I saw this on TV last night.

Me too! That's my favorite channel!
posted by loquacious at 10:56 AM on October 26, 2006

That picture makes me want to slap the side of my computer monitor.
posted by jefbla at 10:59 AM on October 26, 2006

"Pi is exactly three"

x
posted by howfar at 11:04 AM on October 26, 2006

I knew that's what was going to happen. Call it a hunch!
posted by ORthey at 11:13 AM on October 26, 2006

posted by Mister_A
I want to see what i looks like.

One pixel, but your monitor probably won't render octarine.
posted by graymouser at 11:16 AM on October 26, 2006 [2 favorites]

sonofsamiam: as we do not know all the digits of Pi, there is no way to know if it is roughly normally distributed or not. It may so happen that far enough in the sequence it is the number 3 for 10 billion places.

Unless there is a mathematic proof showing non-replicating sequences in Pi. If that is the case, then never mind my butt-talk-outery.

Also, I thought this was a mildly interesting idea. More art than math, which is fine.
posted by Ynoxas at 11:17 AM on October 26, 2006

Did you guys see the dolphins? If you back up and relax your eyes, the dolphins just pop out.
posted by mathowie at 11:18 AM on October 26, 2006

Is this something I'd need to know how to count to understand?
posted by cccorlew at 11:19 AM on October 26, 2006

Like, dude, it's totally a cannabis leaf (inhale)
posted by Rufus T. Firefly at 11:20 AM on October 26, 2006

I can see my house from here!
posted by smackwich at 11:25 AM on October 26, 2006

Ynoxas-
If, as has been posited, the number of decimals in pi is infinite, then it seems that there is a strong possibility that at some point, there IS a stretch of 10 billion consecutive 3s. It's the "1000 monkeys + 1000 typewriters + 1,000,000 years = monkey types full text of Joyce's Ulysses at some point" idea. I know it's probably wrong, but there you have it.

Also - WHat if pi was converted to octal or hex? Does that change it? Know what I mean? Like maybe it's just 3.06 in hex or something...
posted by Mister_A at 11:28 AM on October 26, 2006

In Carl Sagan's Contact, finding stuff in pi is a plot point. Not sure if that made it to the movie version.
posted by smackfu at 11:30 AM on October 26, 2006

But this shows a confined block, and pi is an irrational number, so this is just completely incorrect.
posted by wumpus at 11:31 AM on October 26, 2006

Mister_A -
WHat if pi was converted to octal or hex? Does that change it? Know what I mean? Like maybe it's just 3.06 in hex or something...

Then it would be rational (i.e., something would divide evenly into it). Pi continues forever because it's not rational.
posted by graymouser at 11:33 AM on October 26, 2006

Hey, pi knows my birthday!
posted by brain_drain at 11:34 AM on October 26, 2006

it's not a sailboat, it's a schooner
posted by mikoroshi at 11:38 AM on October 26, 2006

Is pi normal?

How to compute isolated digits of pi
posted by sonofsamiam at 11:39 AM on October 26, 2006 [1 favorite]

So I guess irrational numbers always irrational regardless of what base they are expressed in? Wowee! I'll bet many a dissertation has been written about that. I'm always amazed by people who can grasp concepts like that. Also by people who play the violin real good.
posted by Mister_A at 11:41 AM on October 26, 2006

Did anyone else look at the picture, get a huge headache, then wake up in the Nevada desert covered in blood?

Or is that just me?
posted by robocop is bleeding at 11:42 AM on October 26, 2006 [1 favorite]

from brain_drain's link:

'3' found at position 9 in pi's digits after the decimal point!

Now someone needs to create a web site that searches the digits before the decimal point in pi.
posted by snofoam at 11:42 AM on October 26, 2006

Also, here's a decent Wikipedia article about Contact and the search for meaning in pi. (smackfu, this point wasn't in the movie.)
posted by brain_drain at 11:44 AM on October 26, 2006

It's rational if you are using the number system in the bible (base π/3). Then it's exactly 3.0
posted by MtDewd at 11:44 AM on October 26, 2006

This seems like it would be much better if it has a user interface whereby you could change the width and look for patterns with differing widths.
posted by Monkey0nCrack at 11:46 AM on October 26, 2006

It's a sailboat!

NOTE: I POST ALL COMMENTS WITHOUT READING ANYONE ELSE'S FIRST
posted by rusty at 11:51 AM on October 26, 2006

octarine: not to be confused with infrablack.
posted by quin at 11:53 AM on October 26, 2006

"Now clear your minds. It knows what scares you. It has from the very beginning. Don't give it any help, it knows too much already."
posted by kimota at 11:58 AM on October 26, 2006

Mister-A:

Well, pi would be rational in base pi, or a base that is mathematically related to pi (like base 2πr, or MtDewd's base π/3). But if it were rational in base 4, or 8, or 16, that would mean its irrational digits were evenly divisible by some number; for instance, .1 in hex means 1/16, and .01 means 1/256, so 3.06 base 16 = 3.0234375 base 10. Since it's irrational, it couldn't have a pattern that happens to be divisible by a rational number, even if that rational number were 67A32C7865D...E.
posted by graymouser at 12:00 PM on October 26, 2006

Got it graymouser, thanks!
posted by Mister_A at 12:02 PM on October 26, 2006

"Actually, I thinks it's one of those 3D magic eye pictures, stare at it long enough and unfocus your vision."

Like I really needed to see a 3-D rendition of Bea Arthur nude.
Thanks.
Jerk.
posted by MikeMc at 12:06 PM on October 26, 2006

It would be interesting if there were irrational bases for pi in which it's expansion terminated where the base is not obviously pi-related. With all the weird pi-identities there are, there must be some fun examples.
posted by sonofsamiam at 12:06 PM on October 26, 2006

And if you like this, why not try looking for patterns amongst the prime numbers in an Ulam spiral?
posted by senor biggles at 12:07 PM on October 26, 2006

I wonder if changing the number of pixels per line (ie., change the width of the picture) might not reveal a pattern...
posted by porpoise at 12:12 PM on October 26, 2006

My God...it's full of stars!
posted by darkstar at 12:15 PM on October 26, 2006 [1 favorite]

Following MtDewd, Pi (1 Kings 7:23 version)
posted by quite unimportant at 12:17 PM on October 26, 2006

Pi seems to know my SSN number (in retrospect, I just realized that the site could be an elaborate SSN collection site and now I feel stupid).

*eyes PI suspiciously*
posted by drezdn at 12:18 PM on October 26, 2006 [1 favorite]

It's pretty cool, whatever it is.
posted by OmieWise at 12:24 PM on October 26, 2006

I think pi is a full-scale version of the universe with a little sign that says "You are Here".
posted by Mister_A at 12:32 PM on October 26, 2006

full-scale model that is...
posted by Mister_A at 12:33 PM on October 26, 2006

Rusty: No, it's a schooner.

ME TOO
posted by phearlez at 12:37 PM on October 26, 2006

I always explain irrational numbers as geometric incommensurability. That's not just because of a preference for historical perspective, but because it's much more intuitive and results in real comprehension. I don't think most people who can describe irrationals as "non-repeating, infinite decimal expansions" or even "can't be divided evenly" really grasp what it is they are saying. The geometrical explanation makes this clear. And it's entirely counterintuitive, it makes no damn sense. It's beautiful.
posted by Ethereal Bligh at 12:39 PM on October 26, 2006

Has anybody tried to make a picture of 'e'? Perhaps if you overlay the two you get "ZAPHOD BEEBLEBROX WAS HERE".

That seems highly improbable.
posted by thanotopsis at 12:45 PM on October 26, 2006

Here's a 1024x768 plotting of prime numbers. A dot for prime, black for not prime. 0 is the upper left hand corner, read left to right. Self-linkaroo, but relevant.
posted by unixrat at 12:48 PM on October 26, 2006 [3 favorites]

Lines are just a human construct.
posted by aye at 12:48 PM on October 26, 2006

*drills hole through head*
posted by It's Raining Florence Henderson at 12:55 PM on October 26, 2006

unixrat-That is cool. That is all.
posted by OmieWise at 1:00 PM on October 26, 2006

lordsludge's axiom: For any base irrational, every base rational rational number is irrational.

What do I win?
posted by LordSludge at 1:12 PM on October 26, 2006

LordSludge: 0 is both what you win and the counterexample to your proposition :)
posted by sonofsamiam at 1:16 PM on October 26, 2006

This image is meanlingless for a few reasons:

1. It is plotting the digital base-10 representation of pi which is just one of many number systems.

2. The choosen color scheme is arbitray.

3. The grid size is arbitrary

4. Giving equal weight (pixel size and/or intensity) to each decimal place is meaningless.

You may as well plot the square root of 2.
posted by StarForce5 at 1:40 PM on October 26, 2006 [1 favorite]

Am I the only one who looked at that and said, "huh, that's kinda pretty" and then moved on with my life?

It was an attempt to visualize something that 99% of people are totally unable to visualize on their own.

I think that was the point in its entirety.
posted by InnocentBystander at 1:43 PM on October 26, 2006

I agree with senor biggles, the Prime Spiral rules.
posted by rom1 at 1:54 PM on October 26, 2006

congrats, he has created tv static.
posted by MrLint at 2:22 PM on October 26, 2006

Well on that note, Mr. Innocent Bystander, allow me to point out that all numbers are abstractions. You think just because pi is irrational, it is harder to "visualize"? Wellity.

Since there are more irrational numbers than rational, so allow me to share a link to an attempt at visualizing a member of the underrepresented minoirty of rational numbers. Keep in mind, its only an attempt to help people visualize a certain integer, which 99% of people are totally unable to visualize "on their own".



Hopefully, you can look at that and say, "huh, that's kinda pretty" and then move on with your life?
posted by mano at 2:47 PM on October 26, 2006

damn, the pic isnt showing. here is is, again, and if it dont work, try this link:
http://sprinklebrigade.com/images/gallery/bday.jpg


posted by mano at 2:49 PM on October 26, 2006

Very cool. Large scale randomness, depicted.
posted by MarshallPoe at 3:33 PM on October 26, 2006

damn mallrats! it goes like this:
cute little girl: It's a schooner!
Snowball: It's not a schooner, it's a sailboat.
cute little girl: [sneering] A schooner is a sailboat.
Snowball: [RAGE]
carsonb: [RAGE]
posted by carsonb at 4:14 PM on October 26, 2006

Kind of boring. And thats coming from someone who is a bit obsessed with math.

What he should have done is generate another one using random numbers generated by say radioactive decay and then challenged people to tell which is which.
posted by vacapinta at 4:16 PM on October 26, 2006

Here's a 1024x768 plotting of prime numbers. A dot for prime, black for not prime. 0 is the upper left hand corner, read left to right. Self-linkaroo, but relevant.

I can do you one better: here's a full-screen plot (that resizes dynamically with your browser!) of multiples of ten. Yellow is prime, blue is non-prime.
posted by cortex at 4:44 PM on October 26, 2006

I want one with sliders to adjust:

1. The base;
2. The type of variance (arbitrary rainbow, linear brightness, etc);
3. The shape of the 2d image.

So I could, say, dynamically view all the numbers packed into a circle in base 7 with linear brightness and see noise, but when I hit (say) base 3 I suddenly end up with a white ring around a black center with a smooth gradient in between.

Which would never happen, of course, but what a fun coding exercise...
posted by davejay at 5:01 PM on October 26, 2006

Is it all signal and no noise, or all noise and no signal?
posted by weston at 5:02 PM on October 26, 2006

I'm always boggled a little by the label of Pi as "irrational."

Though I know it isn't rational by the definition of rational numbers, it *is* based on the "ratio" between a circle's circumference and its diameter. That might be mathematically sound reasoning, but it's confusing linguistically.
posted by mrgrimm at 5:11 PM on October 26, 2006

Sure, but one or the other of those numbers—the circumference or the diameter—must necessarily be itself irrational, and so to call that a "ratio" sets us hopping from turtle to turtle to turtle, all the way down.

However, I agree that it feels a little weird. I think this is why they came up with the concept of "transcendental" numbers—to satisfy the linguistic twitch. The mathematical consequences of that discovery are secondary.
posted by cortex at 5:18 PM on October 26, 2006

A picture of Binary Pi
posted by seanyboy at 5:19 PM on October 26, 2006

The shape is wrong. As we all learned in grade school, pi are square, but the top and bottom of the photo are clearly longer than the sides.
posted by diddlegnome at 5:45 PM on October 26, 2006 [1 favorite]

This image is meanlingless

I disagree that it's meaningless, at least for the reasons that are stated. To begin with, unless I'm missing something, it seems to me that a visual interpretation that produces a pattern in one base would produce a pattern in any base whose radix is much much smaller than the number of pixels in the graph. Hence point #1 is not relevant. Regarding the other points, I'd like to see evidence that the variations (choice of color, weight, grid size) mentioned would be likely to obliterate an existing pattern. None of those elements seem capable of making a periodic pattern lose its periodicity, which is what ultimately whether we can ascertain anything with the naked eye. Patterns are very difficult to mask, particularly by accident, much to the delight of cryptographers, crackers and card sharps. So I'm inclined to believe that if pi strongly deviated from a normal distribution, some kind of pattern would likely be evident.


Consider unixrat's prime number image several posts back. There is a clear diagonal pattern which might lead someone to investigate further. That's also true of many patterns generated by pseudorandom generators. Yet pi is apparently all noise. Failing a test is just as meaningful as passing one.

I concede though, the image would be much more interesting if we could dynamically change its underlying variables. It would be illuminating to see no pattern regardless of scale, base and color. It would be exhilarating (and possibly frightening) if a pattern suddenly popped out as we were playing with the sliders.
posted by xigxag at 6:58 PM on October 26, 2006

mmm...pie...
posted by UbuRoivas at 7:20 PM on October 26, 2006

Wow! Even creative and whimsical math is boring!
posted by applemeat at 7:20 PM on October 26, 2006

*drills hole through head*

Survival of the fittest, Max, and we got the fucking gun!
posted by A dead Quaker at 7:45 PM on October 26, 2006

Since I was bored, here are the first 100000 digits in an html file using spans for colour. This way you can resize the flow of the text by resizing the traffic.

Do me a favour though, save the file to your local machine and then open it, so I don't choke on bandwidth. The html file is about 2.4mb.
posted by Kickstart70 at 8:09 PM on October 26, 2006

"That might be mathematically sound reasoning, but it's confusing linguistically."

No, that's the etymology of both uses. See Euclid.
posted by Ethereal Bligh at 8:14 PM on October 26, 2006

btw, a two dimensional image is clearly not how one would want to visualize this, even if they were expecting a clever pattern.

You want to visualize it in four dimensions maybe? Sorry, two is as far as my monitor goes. Not to mention my eyes. And my visual cortex.

(Well, OK, the wetware handles 'two and a half' dimensions, to use Steven Pinker's phrase. But the hardware's still stuck at two.)

Now, I agree that a raster scan is a completely graceless way to build the visual, and one wouldn't expect it to turn out anything interesting. I'd like to see the bits of binary pi in a lovely quasi-spiral, in the manner of Ulam's Rose. Wouldn't you?
posted by eritain at 9:41 PM on October 26, 2006

Oh, and weston wins the prize for awesomest question ever.

If you look at it as an approximation of pi, it's a small amount of signal (since pi is computable by a compact program) plus a lot of redundancy (which may be signal or noise, depending on the receiver's needs). If you look at it as an exact description of a rational number very, very close to pi, or as a series of assertions ('the number I wish to convey equals pi, accurate to plus or minus one', 'the number I wish to convey equals pi, accurate to one tenth', 'the number I wish to convey equals pi, accurate to one one-hundredth', etc.), then it's all signal too. Or if you look at it as a picture of my grandma, then it's all noise. Except the 42nd digit, which looks just like her.
posted by eritain at 9:54 PM on October 26, 2006

Wow! Even creative and whimsical math is boring!
posted by applemeat at 7:20 PM PST on October 26

Its not really creative and its not math. Whimsical? Maybe. Boring? Certainly. Thats what people are saying in this thread.

Irrational numbers are everywhere. If I draw a square, its diagonal is an irrational number too.

I do like this sentence a few posts up:

It would be illuminating to see no pattern regardless of scale, base and color.

Thats true randomness. No pattern no matter how you twist it or massage it or bend it or distort it --- except of course that it's pi.
posted by vacapinta at 10:15 PM on October 26, 2006

What's the state of the art with the assumed randomness of pi vs. Ramsey theory assumptions about the occurance of local patterns? And shit? Inquiring minds, etc.
posted by cortex at 10:18 PM on October 26, 2006

Okay, the pi thing was interesting and all, but this whole thread was worth it to me for this sentence from the link vacapinta mentioned above:

HotBits is an Internet resource that brings genuine random numbers, generated by a process fundamentally governed by the inherent uncertainty in the quantum mechanical laws of nature, directly to your computer in a variety of forms. HotBits are generated by timing successive pairs of radioactive decays detected by a Geiger-Müller tube interfaced to a computer.

OMG, a Geiger counter interfaced to a computer... Measuring the radioactive decay of a piece of rock somewhere... Producing data at 100 Bytes per second... "Fundamentally governed by the inherent uncertainty in the quantum mechanical laws" of the universe?? How can anything be cooler than that? 1950s atomic paranoia + punchcard mainframe + quantum mechanics. I can almost smell the campus lab buildings just thinking about it.
posted by salvia at 1:13 AM on October 27, 2006

Whoa, and that guy co-wrote AutoCAD. Seems like he's a little smart. But can he write science fiction?
posted by salvia at 1:20 AM on October 27, 2006

Hey, I can see my house from here!
posted by jeremias at 4:09 AM on October 27, 2006

Seems like he's a little smart.

You can spend a LOT of time at his site and it won't be wasted. My favorite is his demonstration of universal graviation using only a rope, some rocks, and a piece of wood.
posted by sonofsamiam at 6:52 AM on October 27, 2006

Hoax revealed: pi actually equals 3.0
posted by emanresubmud at 5:18 PM on October 29, 2006