# Factor CongaNovember 1, 2012 8:17 AM   Subscribe

Animation of prime factorization of the integers based on Brent Yorgey's factorization diagrams, described here. [via Data Pointed, previously.]
posted by albrecht (33 comments total) 66 users marked this as a favorite

Terrific! I'll be watching this for the next ten thousand years.
posted by dirtdirt at 8:27 AM on November 1, 2012 [3 favorites]

My mom is going to love this. She's a math teacher and really enjoys showing visual mathy things to her 7th and 8th graders.
posted by cranberry_nut at 8:31 AM on November 1, 2012 [1 favorite]

Nice. I read years ago that the secret to lulling an insomniac brain to sleep is some basic activity that engages both sides of the brain (something visual, something methodical). Counting sheep is the classic example; for years I have been imagining writing the numbers from one to one hundred on a chalkboard. This might replace it for me.
posted by ricochet biscuit at 8:31 AM on November 1, 2012 [1 favorite]

I love this. I would love it even more if the data (the numbers & whether they are prime or their factors) were in the center, where I could see the more easily than way up in the left corner.
posted by chavenet at 8:41 AM on November 1, 2012 [3 favorites]

Huh. I watched it for ten minutes, then noticed a pattern that predicts exactly when the next prime will appear. Too bad I don't have time to post it right now. :-( I'm late for my BASE jumping class! Gotta run!
posted by Zerowensboring at 8:48 AM on November 1, 2012 [47 favorites]

Huh. I watched it for ten minutes, then noticed a pattern that predicts exactly when the next prime will appear. Too bad I don't have time to post it right now

It was probably too long to fit in the metafilter comment box anyway.
posted by Philosopher Dirtbike at 8:52 AM on November 1, 2012 [12 favorites]

Huh. I watched it for ten minutes, then noticed a pattern that predicts exactly when the next prime will appear.

I only watched the first few, but I think I saw the same pattern: 3 is prime, 5 is prime, 7 is prime, etc.
posted by albrecht at 9:01 AM on November 1, 2012 [17 favorites]

Psychedelica mathematica.
posted by marienbad at 9:05 AM on November 1, 2012

It was probably too long to fit in the metafilter comment box anyway.

It would have fit all right, but the edit margin was too small.
posted by tykky at 9:05 AM on November 1, 2012 [3 favorites]

I smirked at Zerowensboring's gag, and my next thought was how pleased they'd be to find how many favorites that comment had garnered. You know, upon returning from BASE jumping class.
posted by phl at 9:07 AM on November 1, 2012

Powers of three are especially fun, since their factorization diagrams are Sierpinski triangles!

This observation really deserves that exclamation mark.
posted by wachhundfisch at 9:15 AM on November 1, 2012 [2 favorites]

Oooh, just noticed there's a FF transport on the lower right! I'm gonna let this run for a few hours... Also, checking out the source, it's nice to find that the main div id = "enchilada".
posted by joecacti at 9:38 AM on November 1, 2012

albrecht: Huh. I watched it for ten minutes, then noticed a pattern that predicts exactly when the next prime will appear.

I only watched the first few, but I think I saw the same pattern: 3 is prime, 5 is prime, 7 is prime, etc.
9 is an outlier, 11 is prime, 13 is pr...
posted by IAmBroom at 9:44 AM on November 1, 2012 [2 favorites]

Primes are unbroken whole circles

Each prime number p is drawn as colored dots on the vertices of a regular polygon of p sides. The larger primes look like circles because there are no edges connecting the vertices to make it obvious.

The composite numbers are drawn the same way, starting with the smallest prime factor. Instead of colored dots, the next largest prime factor places the shape created by the previous prime factor on the vertices of it's new polygon. This is what creates the self similarity, and is why the 2's are always grouped together into squares (even powers of 2 are like Sierpinski gaskets).
posted by grog at 9:47 AM on November 1, 2012 [2 favorites]

The composite numbers are drawn the same way, starting with the smallest prime factor. Instead of colored dots, the next largest prime factor places the shape created by the previous prime factor on the vertices of it's new polygon.

Right.

This is what creates the self similarity, and is why the 2's are always grouped together into squares (even powers of 2 are like Sierpinski gaskets).

Actually, the 2s are handled slightly differently; squares do not just naturally emerge from the algorithm as it works for the other numbers. For other possible factors, each group of dots (or groups) is in a consistent orientation, but with 2-groups, the orientation varies depending on the orientation of the available space for that group. That produces squares; if it weren't for that, two successive 2-groups would form a straight line.

This special-casing makes it prettier (and gives us the cantor dust for powers of 2), but a little more confusing (I tried to figure out what was going on at first just by watching the animation, but the squares had me stumped) until you read the explanation.
posted by a snickering nuthatch at 10:04 AM on November 1, 2012 [2 favorites]

posted by MangyCarface at 10:10 AM on November 1, 2012

Goes really well with Fingertips.
posted by RobotVoodooPower at 10:24 AM on November 1, 2012

The prime number shitting bear should be updated http://alpha61.com/primenumbershittingbear/
posted by ryoshu at 10:25 AM on November 1, 2012 [4 favorites]

SPOILER ALERT: it only goes to 10,000
posted by dubold at 10:28 AM on November 1, 2012 [2 favorites]

This is great. You can see why 6 is my favorite number base.
posted by wobh at 10:29 AM on November 1, 2012

It was probably too long to fit in the metafilter comment box anyway.

I guess it will still be a mystery in the 24th century.
posted by RonButNotStupid at 10:36 AM on November 1, 2012

SPOILER ALERT: it only goes to 10,000

I'm pretty sure there aren't any higher than that anyway.
posted by phl at 10:39 AM on November 1, 2012 [2 favorites]

No one would ever need more than 10,000 numbers anyway. Especially if a lot of them are primes!
posted by blue_beetle at 10:50 AM on November 1, 2012 [2 favorites]

My mind immediately tried to intuit a feel for the rhythm of the prime numbers, so it's probably a good thing I turned this off before I become that guy from the movie pi.
posted by mrgoat at 10:51 AM on November 1, 2012 [4 favorites]

Screen saver want!
posted by eggkeeper at 11:11 AM on November 1, 2012 [1 favorite]

SPOILER ALERT: it only goes to 10,000

I'm pretty sure there aren't any higher than that anyway.

Untrue--24 is the highest number.
posted by Zerowensboring at 12:18 PM on November 1, 2012 [3 favorites]

posted by Cranberry at 12:24 PM on November 1, 2012

I was wondering how the hell they got the alignment so even and precise every time, then I realized every set is a circle whose center is a point equidistant to other points on the perimeter of a larger circle. And the dots are circles too and their centers are also points so arranged. DUH.

Is there a proposition in set theory that every discrete entity is a member of the set of all items that are itself? Would that even be worth stating?
posted by clarknova at 1:41 PM on November 1, 2012

The powers of 3 are great! Note the famously awesome pattern beginning at 2187. [You can click the fast-forward button more than once to get it to really speed up.]
posted by klausman at 1:51 PM on November 1, 2012

On review...what grog said, but about triangles.
posted by klausman at 1:55 PM on November 1, 2012

That's really nice. I wished that the start/stop actually took you to the nearest integer. I kept stopping in the middle of the transition.
posted by leahwrenn at 2:07 PM on November 1, 2012

I didn't expect to see this here! I went to junior and high school with Brent, we studied CS together 15 years ago. He's insanely talented in maths but music as well, which has clearly passed down to his kid. I'll ping him on Facebook, see what he has to say.
posted by now i'm piste at 11:36 PM on November 1, 2012 [2 favorites]

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