[HN Gopher] Animated Factorization (2012)
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Animated Factorization (2012)
Author : miniBill
Score : 215 points
Date : 2025-05-21 14:39 UTC (8 hours ago)
(HTM) web link (www.datapointed.net)
(TXT) w3m dump (www.datapointed.net)
| chrsw wrote:
| This looks cool. Could also be a screensaver (do people still use
| those)?
| apples_oranges wrote:
| Macs now have them again. OLED screens made them create
| animated login screens. (At least I think that's what
| happened.)
| pvg wrote:
| Threads (with some explainy links) from a million and a million
| and a bit years ago
|
| https://news.ycombinator.com/item?id=10776019
|
| https://news.ycombinator.com/item?id=4788224
| sherdil2022 wrote:
| And definitely re-post worthy!
| dang wrote:
| Thanks! Macroexpanded:
|
| _Factorizer_ - https://news.ycombinator.com/item?id=10776019 -
| Dec 2015 (30 comments)
|
| _Animated Factorisation Diagrams_ -
| https://news.ycombinator.com/item?id=4788224 - Nov 2012 (72
| comments)
|
| _Animated Factorization Diagrams_ -
| https://news.ycombinator.com/item?id=4713048 - Oct 2012 (2
| comments)
| math_dandy wrote:
| The diagrams for powers of three form the Sierpinski triangle.
| Makes total sense once you see it, but I hadn't seen it until
| today!
| robot_jesus wrote:
| Same. I loved this unique insight that the visualization
| provided. It definitely unlocked something in my brain for how
| I should think about that shape.
|
| If anyone is curious, 6561 (3^8) is the highest pure Sierpinski
| available in the animation since it caps at 10K.
| blueflow wrote:
| I thought this was a waiting animation and the website is broken.
| kccqzy wrote:
| It would function pretty well as a waiting animation too.
| nurumaik wrote:
| Waiting animation that ends after the last prime number
| simojo wrote:
| it took me a few seconds before I realized that it wasn't the
| page loading
| worldsayshi wrote:
| This is brilliant!
|
| Now i want (to build) a drag and drop toy where i can multiply or
| summarize numbers that are represented in this way. To see how
| factors move (like boids).
|
| Is this visualization algorithm called something? The explanation
| link from a previous HN post seems to be broken:
| http://mathlesstraveled.com/2012/10/05/factorization-diagram...
| CGMthrowaway wrote:
| Kind of makes me wish that there were recognizable shapes for
| primes bigger 2 (pair), 3 (triangle), 4 (square) and 5
| (pentagon) that didn't just look like circles. Because my
| favorite part about this is how you can see at a glance what
| the factors are. Except for primes 7 or greater I find myself
| cheating and looking at the top left for which prime it is.
|
| Is there some non-regular polygon that would be more distinctly
| recognizable to use for 7, 11, etc?
| GaggiX wrote:
| Aren't 2 (pair), 3 (triangle), 4 (square) and 5 (pentagon)
| also "circles" with less resolution? The visualization is
| just consistent.
| CGMthrowaway wrote:
| Yes I dont disagree and it is elegant as is, but the way
| our eyes/ brain works it's much harder to ID septagon,
| nonagon, triacontahenagon etc at a glance. A non-regular
| shape would be better fit for purpose
| worldsayshi wrote:
| Couldn't you draw it in a recognizable way using summation?
|
| 7 = 2*3+1
|
| 11 = (2*2+1)*2+1
|
| etc...
| CGMthrowaway wrote:
| Interesting idea
| Liftyee wrote:
| Agree. I watched for a while to see some larger primes and
| was a little disappointed.
|
| Filled polygons would offer some more shapes. Filled hexagon
| = 7, etc etc...
| drdeca wrote:
| 4 isn't prime.
|
| You could probably use the binary expansion to group the
| dots? So, 1 is * 2 is ** 3 is _* *_*
|
| 5 is
|
| _* *_* *_*
|
| 7 is ____* _*_____* *_*___*_*
|
| 11 is ____* _*_____* *_*___*_* *_*___*_*
|
| And so on.
|
| (So, 2n is represented as n next to n, unless n is 2 in which
| case it is n above n, and 2n+1 is 1 above 2n )
|
| Alternatively, using stars instead of n-gons could also be
| clearer?
| ashwinsundar wrote:
| I believe it's called prime factorization. Each number is
| placed in a group of numbers (or group of groups, etc...)
|
| E.g. 24 -> 2 * 3 * 4 = Two groups of (three groups of (four
| items))
|
| Also try this for the archived version of that explanation ->
| https://web.archive.org/web/20130206023100/http://mathlesstr...
| ajjenkins wrote:
| This would make a cool progress bar replacement. Replace
| percentage with the number of dots (0-100).
| tocs3 wrote:
| It makes me wonder what the algorithm for arranging the dots
| looks like.
| GrantMoyer wrote:
| 1. Set var factors to the prime factors of the integer
|
| 2. Sort factors in ascending order
|
| 3. Set var diagram to a single dot
|
| 4. Foreach factor in factors
|
| 4.1. Set var diagram to factor copies of diagram aranged in a
| circle
| tocs3 wrote:
| I was thinking about triangles and squares and the answer was
| circles.
| andrewrn wrote:
| This is very cool. It looks like you used the canvas api for
| this, but I had expected that you'd use D3.js since its so common
| for data visualizations. I am curious what your thinking was
| there?
| pona-a wrote:
| But it's not CRUD data visualization, it's a custom animation.
| Why use a heavy library if the browser draws circles just fine?
| aaroninsf wrote:
| I wish that all the factors were shown,
|
| e.g. when on 12, I'd like to see both 3x4 and 2x6, with a visual
| indicator of when the animation is showing the different
| factors... maybe the whole thing shrinks and additional
| factorizations fill in tiles subdividing the space
|
| Knowing the number of different factorizations is an interesting
| and visually presentable quality that interacts in an interesting
| way with the factors themselves
| gus_massa wrote:
| Slightly related: If you have small kids, I recommend
| https://www.youtube.com/@Numberblocks that is a cartoon that has
| characters that are numbers made by blocks, and they split to
| show sum and rearrange to show the factorization. It's fun for
| kids and the technical part is correct.
| carterschonwald wrote:
| I think this was originally invented by Brent yorgey
| kccqzy wrote:
| I wish the animation could play at a slower pace so you have time
| to count the number of groups and the circles within each group.
| I also wish each time a new circle would animate from the edge of
| the screen and then arranged to show the addition of the new
| circle clearly. Otherwise, excellent visualization!
| gavmor wrote:
| The jumps between neighbors are sometimes so drastic--are we sure
| our numbers are in the right order?
| jhanschoo wrote:
| I don't know what you mean by that, but for an example, 16=2^4
| and is therefore arranged as a grid, whereas 17 is prime, and
| must therefore be arranged as 17 dots on a circle.
| gavmor wrote:
| The primes _are_ some of the worst offenders, eg the
| transition from 647 (prime) to 648 (3x3x3x3x2x2x2), but as we
| approach infinity, the visualizations increasingly appear
| circular, and it 's the least-primey (?) that break from the
| trend.
|
| eg 854-856, & 857 (prime) are all virtually or perfectly
| circular. Or maybe I'm observing not mathematical but neuro-
| visual principles.
| jerf wrote:
| That's the difference between the additive view of the world
| and the multiplicative one. A lot of number theory involves
| trying to bridge that gap, and even this simplest view of
| numbers can rapidly fling you into the mathematical unknown.
| The "simplest hard problem", the Collatz conjecture, can be
| viewed as coming from this space. You either take a step in
| multiplicative space, or a step in multiplicative space and
| then additive space, and ask a very simple question about where
| those steps can take you.
|
| And that's all it takes to end up at an unsolved problem in
| math.
|
| You can spend a lifetime on this simple observation that "the
| jumps between neighbors are so dramatic", just trying to
| reconcile the complex relationships between the additive view
| of the world and the multiplicative one.
|
| And we haven't even done anything like bring in complex
| numbers, or rationals, or introduce exponentiation!
| gavmor wrote:
| How can a layperson approach and develop correct intuitions
| for "the multiplicative view" of numbers? Is it practical?
| jderick wrote:
| Can you put them all on one page and zoom in/out? Might be
| interesting to see some patterns in the sequence. Maybe allow
| filters for different factors or number ranges or different
| groupings.
| vivzkestrel wrote:
| sliders should be added on this page that control everything.
| colors and speed are starters
| ttoinou wrote:
| This is pure genius, congrats, and I'm disappointed at myself I
| didn't think about that earlier (:
| liendolucas wrote:
| This is cool! Lets use it to display the digits of a clock :-)
| ape4 wrote:
| I think the sum of the area of the circles should remain
| constant. ie be the number that's being factored.
| glaucon wrote:
| Really good. I would appreciate it if it could be slowed down, or
| allow the numbers to be stepped through.
| dtjohnnymonkey wrote:
| After some time I find myself waiting for highly composite
| numbers rather than primes.
| smusamashah wrote:
| Does it let you put your own number and see what diagram it
| makes?
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