4 ms·

Prime Number Visualization Simulation Spiral

82 points by gulbrandr 14y ago

digitalboss 14y ago
Nice job. - I would suggest re-labling the btm controls to say "Left/RIght for Slower/Faster"
PaperclipTaken 14y ago
It's an interesting visualization, but it doesn't really seem to highlight anything new about the way prime numbers are structured. It's difficult to make connections between the spiral and the prime numbers, because the red pieces don't generally stand out strongly against the white pieces (at least not in any obvious pattern. There are cool things you can notice if you think about it long enough, but you notice these things without the help from the spiral too).
- happyglucky 14y ago
  Visualizations aren't meant to highlight anything new, but rather to bring to light and visualize what is already known.
  - SeanLuke 14y ago
    What exactly is already known that this visualization is bringing to light?
    - happyglucky 14y ago
      A number of very elementary things. It gives a very intuitive visualization of twin primes, as they lie before and after highly composite numbers (which are also easily visualized), as well as a visual explanation for why the prime gaps tend to increase, as larger numbers are likely to collide with a factor. You can also use it to explain prime factors, least common multiples up to N (when the first N lines come into alignment), and the cyclical nature of factors in general. This is a creative pedagogical tool, not a breakthrough in number theory.
      - SeanLuke 14y ago
        I'm sorry but I don't see how this visualization provides any special insight into any of these things.
        tripngroove 14y ago
        You can literally see the aforementioned concepts if you observe the visualizer.
  - jlarocco 14y ago
    I disagree with that. The entire point of data visualization is to highlight patterns in data to make the data easier to understand. Highlighting what's already known is a waste of time. A good visualization will help uncover something new. I feel bad saying this, because it probably took a lot of work to make, but this prime number spiral is kind of pointless. What is it showing me? If I let the painfully slow animation run for a while, and look at the bigger picture, what insight will I gain about prime numbers? Probably nothing. It's even a bit misleading, because to the best of my knowledge, there's no connection between spirals and prime numbers. If I'm just being dense and not getting it, I'd love for somebody to explain it to me.
    - happyglucky 14y ago
      "there's no connection between spirals and prime numbers" You just shot yourself in the foot :( Yes, there is a connection. If you add up the total distance each line makes in a tick, its equivalent to the harmonic series, which is a special case of the zeta function. This is where the spiral comes from. Its a dirct consequence of the fact that each number has period 1/n. The spiral emerges naturally, its not programmed or forced into that shape.
      - jlarocco 14y ago
        If that's the concept the visualization was trying to get across, then it failed pretty bad. It may look neat, but it doesn't make any of those connections apparent.
darklajid 14y ago
I love it. And as sad as it is that I have to point this out specifically: This site works awesome from this guy's couch on an Android device.
sabalaba 14y ago
Another great visualization of the primes is the famous Ulam spiral: http://upload.wikimedia.org/wikipedia/commons/6/69/Ulam_1.png http://upload.wikimedia.org/wikipedia/commons/6/69/Ulam_1.pn...
kzahel 14y ago
It's a very beautiful visualization. I particularly enjoy seeing the period of each block correspond with the representative number. If only there were more visualizations like this for other mathematical concepts!
robbiep 14y ago
I wasn't aware of this. Thank you. I understand better what people mean when they say primes are fractal now
fumar 14y ago
I found this to be a great visual. I stared at it for quiet some time looking for the patterns. I thought it would be cool to put some music to it... https://www.youtube.com/watch?v=hnHhRtHmiCc https://www.youtube.com/watch?v=hnHhRtHmiCc Edit: I will go back and fine tune the video so it syncs to the music.
kmm 14y ago
Very cool! Too bad it's not possible to rewind though.
- ggchappell 14y ago
  It is possible. Hit the "backward" button at the top.
  - kmm 14y ago
    Woah, that did not exist yet when I made my comment. Thanks.
bjxrn 14y ago
Here's another prime number circle/visualization: http://www.flickr.com/photos/michaelpaukner/3977033600 http://www.flickr.com/photos/michaelpaukner/3977033600 The creator of that one links to a Geocities page (which doesn't exist anymore, of course), but I think that page probably moved here: http://www.magic-squares.net/moreprimes.htm#A%20Prime%20Circle http://www.magic-squares.net/moreprimes.htm#A%20Prime%20Circ...
denzil_correa 14y ago
Another Prime Number Pattern Visualization by Jason Davies which was posted on HN sometime back. http://www.jasondavies.com/primos/ http://www.jasondavies.com/primos/
FWeinb 14y ago
A while ago I recreated the visualization of the Sieve of Eratosthenes from Wikipedia (http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes) in Javascript: http://codepen.io/FWeinb/full/tmwnf http://codepen.io/FWeinb/full/tmwnf

82 points by gulbrandr 14y ago

Nice job. - I would suggest re-labling the btm controls to say "Left/RIght for Slower/Faster"

It's an interesting visualization, but it doesn't really seem to highlight anything new about the way prime numbers are structured. It's difficult to make connections between the spiral and the prime numbers, because the red pieces don't generally stand out strongly against the white pieces (at least not in any obvious pattern. There are cool things you can notice if you think about it long enough, but you notice these things without the help from the spiral too).

happyglucky 14y ago
Visualizations aren't meant to highlight anything new, but rather to bring to light and visualize what is already known.
- SeanLuke 14y ago
  What exactly is already known that this visualization is bringing to light?
  - happyglucky 14y ago
    A number of very elementary things. It gives a very intuitive visualization of twin primes, as they lie before and after highly composite numbers (which are also easily visualized), as well as a visual explanation for why the prime gaps tend to increase, as larger numbers are likely to collide with a factor. You can also use it to explain prime factors, least common multiples up to N (when the first N lines come into alignment), and the cyclical nature of factors in general. This is a creative pedagogical tool, not a breakthrough in number theory.
    - SeanLuke 14y ago
      I'm sorry but I don't see how this visualization provides any special insight into any of these things.
      - tripngroove 14y ago
        You can literally see the aforementioned concepts if you observe the visualizer.
- jlarocco 14y ago
  I disagree with that. The entire point of data visualization is to highlight patterns in data to make the data easier to understand. Highlighting what's already known is a waste of time. A good visualization will help uncover something new. I feel bad saying this, because it probably took a lot of work to make, but this prime number spiral is kind of pointless. What is it showing me? If I let the painfully slow animation run for a while, and look at the bigger picture, what insight will I gain about prime numbers? Probably nothing. It's even a bit misleading, because to the best of my knowledge, there's no connection between spirals and prime numbers. If I'm just being dense and not getting it, I'd love for somebody to explain it to me.
  - happyglucky 14y ago
    "there's no connection between spirals and prime numbers" You just shot yourself in the foot :( Yes, there is a connection. If you add up the total distance each line makes in a tick, its equivalent to the harmonic series, which is a special case of the zeta function. This is where the spiral comes from. Its a dirct consequence of the fact that each number has period 1/n. The spiral emerges naturally, its not programmed or forced into that shape.
    - jlarocco 14y ago
      If that's the concept the visualization was trying to get across, then it failed pretty bad. It may look neat, but it doesn't make any of those connections apparent.

darklajid 14y ago

I love it. And as sad as it is that I have to point this out specifically: This site works awesome from this guy's couch on an Android device.

sabalaba 14y ago

Another great visualization of the primes is the famous Ulam spiral: http://upload.wikimedia.org/wikipedia/commons/6/69/Ulam_1.png http://upload.wikimedia.org/wikipedia/commons/6/69/Ulam_1.pn...

kzahel 14y ago

It's a very beautiful visualization. I particularly enjoy seeing the period of each block correspond with the representative number. If only there were more visualizations like this for other mathematical concepts!

robbiep 14y ago

I wasn't aware of this. Thank you. I understand better what people mean when they say primes are fractal now

fumar 14y ago

I found this to be a great visual. I stared at it for quiet some time looking for the patterns. I thought it would be cool to put some music to it... https://www.youtube.com/watch?v=hnHhRtHmiCc https://www.youtube.com/watch?v=hnHhRtHmiCc Edit: I will go back and fine tune the video so it syncs to the music.

kmm 14y ago

Very cool! Too bad it's not possible to rewind though.

ggchappell 14y ago
It is possible. Hit the "backward" button at the top.
- kmm 14y ago
  Woah, that did not exist yet when I made my comment. Thanks.

bjxrn 14y ago

Here's another prime number circle/visualization: http://www.flickr.com/photos/michaelpaukner/3977033600 http://www.flickr.com/photos/michaelpaukner/3977033600 The creator of that one links to a Geocities page (which doesn't exist anymore, of course), but I think that page probably moved here: http://www.magic-squares.net/moreprimes.htm#A%20Prime%20Circle http://www.magic-squares.net/moreprimes.htm#A%20Prime%20Circ...

denzil_correa 14y ago

Another Prime Number Pattern Visualization by Jason Davies which was posted on HN sometime back. http://www.jasondavies.com/primos/ http://www.jasondavies.com/primos/

FWeinb 14y ago

A while ago I recreated the visualization of the Sieve of Eratosthenes from Wikipedia (http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes) in Javascript: http://codepen.io/FWeinb/full/tmwnf http://codepen.io/FWeinb/full/tmwnf