5 ms·

Ulam Spiral

71 points by theunamedguy 10y ago

dang 10y ago
Previous discussions at https://hn.algolia.com/?query=Ulam%20Spiral%20points%3E10&sort=byDate&dateRange=all&type=story&storyText=false&prefix&page=0 https://hn.algolia.com/?query=Ulam%20Spiral%20points%3E10&so....
kordless 10y ago
There's probably code in there, somewhere.
eggy 10y ago
Here is a YouTube video of a breakdown of manually exploring the Ulam Spiral in the J programming language [1], and finally coding it up user tangentstorm. [2] After all, J is an array-processing beast! [1] jsoftware.com [2] https://www.youtube.com/watch?v=dBC5vnwf6Zw https://www.youtube.com/watch?v=dBC5vnwf6Zw
dokument 10y ago
Three years ago I proposed using Ulam Spirals as the peering logic for Bitmessage (decentralized, trustless messenger service). Essentially with Bitmessage you trade messages with everyone on your network but you can be a member of multiple networks. My proposal was to be in one network but peer with with all the "touching" digit peers according to the Ulam Spiral. The benefit of this approach is that newer (higher value) networks are peering with older more established ones and there are multiple paths between non-touching networks to send messages. Here is the forum post with the suggestion: https://bitmessage.org/forum/index.php?topic=2549.0 https://bitmessage.org/forum/index.php?topic=2549.0
- elcct 10y ago
  What has happened since then?
some1else 10y ago
I used it in one of the Pictur Bale pieces (Christian Bale vs. Mathematics GIFs) http://picbale.tumblr.com http://picbale.tumblr.com
graedus 10y ago
Some nice images of a hexagonal version here, along with a python script to create your own: http://hexnet.org/content/hexagonal-number-spirals http://hexnet.org/content/hexagonal-number-spirals
Razengan 10y ago
As someone who occasionally contemplates upon the Origin of Everything (something that I think every sapient being does at least once), looking at the Ulam Spiral felt like there was a faint inspiration just waiting outside the grasp of my understanding; What if Reality came into existence simply out of mathematical truths and the patterns arising from them? That would require no First Cause. And of course, there would be multiple ways to "see" those patterns, with our universe being just one of those ways, just as the Ulam Spiral being a specific 2D ordering of primes. I said "came into existence" but it may be more accurate to say that all perceived existence is just one interpretation or another, of fundamental truths.
- kr0 10y ago
  Wonderfully worded. I'd throw that to Bill Nye at big think on youtube at see what he has to say. He loves "far out there" explanations for everything like that
  - zaaakk 10y ago
    or he could ask an academically trained philosopher of mathematics and probably receive a much more insightful response
- JorgeGT 10y ago
  This reminds me of what Pythagoras believed, Number being an universal archetype, "the principle, source, and root of all things". http://science.jrank.org/pages/10928/Pythagoreanism-Number-Cosmos-Harmony.html http://science.jrank.org/pages/10928/Pythagoreanism-Number-C...
- matthewtoast 10y ago
  I like this insight, but it doesn't overcome the argument for a first cause because you'd still need to explain where those fundamental truths came from.
silveira 10y ago
https://github.com/silveira/ulam https://github.com/silveira/ulam Here is a reusable implentation in Javascript using Html5 canvas. You can just download the source, edit and run in your browser. Or see live examples here: http://silveiraneto.net/2013/05/14/twin-primes-visualized-over-an-ulam-spiral-in-html5/ http://silveiraneto.net/2013/05/14/twin-primes-visualized-ov...

71 points by theunamedguy 10y ago

dang 10y ago

Previous discussions at https://hn.algolia.com/?query=Ulam%20Spiral%20points%3E10&sort=byDate&dateRange=all&type=story&storyText=false&prefix&page=0 https://hn.algolia.com/?query=Ulam%20Spiral%20points%3E10&so....

kordless 10y ago

There's probably code in there, somewhere.

eggy 10y ago

Here is a YouTube video of a breakdown of manually exploring the Ulam Spiral in the J programming language [1], and finally coding it up user tangentstorm. [2] After all, J is an array-processing beast! [1] jsoftware.com [2] https://www.youtube.com/watch?v=dBC5vnwf6Zw https://www.youtube.com/watch?v=dBC5vnwf6Zw

dokument 10y ago

Three years ago I proposed using Ulam Spirals as the peering logic for Bitmessage (decentralized, trustless messenger service). Essentially with Bitmessage you trade messages with everyone on your network but you can be a member of multiple networks. My proposal was to be in one network but peer with with all the "touching" digit peers according to the Ulam Spiral. The benefit of this approach is that newer (higher value) networks are peering with older more established ones and there are multiple paths between non-touching networks to send messages. Here is the forum post with the suggestion: https://bitmessage.org/forum/index.php?topic=2549.0 https://bitmessage.org/forum/index.php?topic=2549.0

elcct 10y ago
What has happened since then?

some1else 10y ago

I used it in one of the Pictur Bale pieces (Christian Bale vs. Mathematics GIFs) http://picbale.tumblr.com http://picbale.tumblr.com

graedus 10y ago

Some nice images of a hexagonal version here, along with a python script to create your own: http://hexnet.org/content/hexagonal-number-spirals http://hexnet.org/content/hexagonal-number-spirals

Razengan 10y ago

As someone who occasionally contemplates upon the Origin of Everything (something that I think every sapient being does at least once), looking at the Ulam Spiral felt like there was a faint inspiration just waiting outside the grasp of my understanding; What if Reality came into existence simply out of mathematical truths and the patterns arising from them? That would require no First Cause. And of course, there would be multiple ways to "see" those patterns, with our universe being just one of those ways, just as the Ulam Spiral being a specific 2D ordering of primes. I said "came into existence" but it may be more accurate to say that all perceived existence is just one interpretation or another, of fundamental truths.

kr0 10y ago
Wonderfully worded. I'd throw that to Bill Nye at big think on youtube at see what he has to say. He loves "far out there" explanations for everything like that
- zaaakk 10y ago
  or he could ask an academically trained philosopher of mathematics and probably receive a much more insightful response
JorgeGT 10y ago
This reminds me of what Pythagoras believed, Number being an universal archetype, "the principle, source, and root of all things". http://science.jrank.org/pages/10928/Pythagoreanism-Number-Cosmos-Harmony.html http://science.jrank.org/pages/10928/Pythagoreanism-Number-C...
matthewtoast 10y ago
I like this insight, but it doesn't overcome the argument for a first cause because you'd still need to explain where those fundamental truths came from.

silveira 10y ago

https://github.com/silveira/ulam https://github.com/silveira/ulam Here is a reusable implentation in Javascript using Html5 canvas. You can just download the source, edit and run in your browser. Or see live examples here: http://silveiraneto.net/2013/05/14/twin-primes-visualized-over-an-ulam-spiral-in-html5/ http://silveiraneto.net/2013/05/14/twin-primes-visualized-ov...